But now they can actually feel what it's like to be right inside by wearing virtual reality (VR) headsets and getting a 360-degree view.
What's more, their colleagues also wearing headsets can inhabit the same life-like model and suggest and make changes to the design in real time. And these colleagues could be on the other side of the world.
This is the exciting new world of virtual buildings - a significant development for an industry traditionally more interested in bricks than clicks.
Even Crossrail chief executive Andrew Wolstenholme admits: "Historically, we have been very slow to pursue innovation. Before, there was no real need for suppliers to change.
"But now, as we have to find more opportunities overseas, we are in a much better place to reap the rewards."
Building information modelling (BIM) - developing a 3D digital prototype of a project - is moving up a gear.
San Francisco-based Vizerra, has introduced "gamification" and VR capability to its BIM product, Revizto.
"Revizto uses 3D gaming technology and cloud solutions to bring together various building design environments and workflows into a single, navigable view," says chief executive Arman Gukasyan.
The software's interactive 3D environments allow users to navigate their sites like in a video game, highlighting structural issues as they explore. Revizto now supports the HTC Vive and Oculus VR headsets.
The project team can collaborate in real time with the help of the built-in Revizto Issue tracker, and assign tasks to each other.
Vizerra says this kind of approach helps save its clients up to 40% of billable time, because errors - inadequate lighting or awkward placing of support columns, for example - can be spotted before construction begins.
"In any construction project 30% or more of total budget is spent on correcting the errors not visible in the design stage," says Mr Gukasyan.
"It is crazy how much money is wasted because of the old standards, where everything is done on 2D paper drawings.
"We are positioning ourselves as disruptive technology which demonstrates how gaming technology can be used in most serious industries and transform the way people co-ordinate and collaborate."
Revizto is now used by more than 60,000 clients in 150 countries, says Vizerra, including global architectural and construction practices, such as Foster & Partners and Perkins & Will.
Other leaders in this rapidly growing market include AutoCAD, Revit and Vectorworks Architect, with Research & Markets forecasting that software sales will reach nearly $12bn (Â£10bn) by 2022.
Large construction projects can be massively complex and costly, so keeping track of workers, materials and the build progress is crucial.
In the past, site foremen would often log staff hours manually in a little black book, which would later be transcribed on to a timecard and then the data fed into a computer.
But data analytics start-up Rhumbix digitises the collection of this data right from the start.
Its app enables staff to submit digital timesheets via smartphone for instant approval by foremen, who can also analyse staff GPS location data to track what work was done where. This makes it easier to pinpoint delays.
Rhumbix co-founder Zach Scheel served as a civil engineer for the US military and drew inspiration from how the army monitored movements of its 3,000 troops stationed at a military base outside Djibouti City during the Arab Spring of 2011.
Working on infrastructure projects a few years later in Chile, Mr Scheel realised there were similar issues with data collection and productivity in the construction sector.
"Labour is the largest cost on project sites and the least well-understood," he says.
"Smartphones, tablets and wireless connectivity have changed the game by laying the technological foundation necessary to build software for the field - where construction happens."
The software also enables the cost, quantity and availability of materials to be recorded in real time and viewed online by project managers. Contractors can also supply their costings and budgets.
This is important because 15% of materials delivered to construction sites end up in landfills, says the UK's Green Building Council, while building-related waste makes up almost 40% of total solid waste in the US.
For a large construction project to operate smoothly you need everyone singing from the same hymn sheet. But in the old analogue world, this was often tricky to achieve - mistakes would creep in.
"We would realise that many of the mistakes were happening because the site engineers did not have access to the right information at the right time," says Alexander Siljanovski, an engineer and chief executive of BaseStone, a software company specialising in construction.
The firm's tablet and web-based collaboration tool digitally links construction sites to head offices, enabling early detection of problems and more effective communications.
Drawings and documents are linked into the system, and new versions are automatically detected.  Before such tools, team members would sometimes find themselves working from out-of-date drawings, or struggling to log safety issues effectively, says Mr Siljanovski.
BaseStone's "digital delivery platform for construction" is used in 50 countries, with clients including Alstom, Skanksa, Balfour Beatty and Crossrail.
Other companies offering similar project management software include HBXL and Builk.
So the construction sector is gradually beginning to appreciate the benefits of digitalisation, and with the help of VR computer-aided design, creating buildings that could never have been built before.
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Architects and construction companies have been able to "look around" computerised 3D models of their buildings for some time.