A new analytical theory for multiple scattering of cylindrical acoustic waves by an array of finite impedance semi-cylinders embedded in a smooth acoustically hard surface is derived by extending previous results for plane waves [Linton and Martin, J. Acoust. Soc. Am. 117 (6) 3413 – 3423 (2005)]. Although the computational demands of the new theory increase as the number of the semi-cylinders in the arrays and/or the frequency increases, the theory offers an improvement on analytical boss theories since the latter (i) are restricted to non-deterministic (infinite) random distributions of semi-cylinders with spacing/radii small compared to the incident wavelength and (ii) are derived only for plane waves. The influence on prediction accuracy of truncation of the infinite system of equations introduced by the new theory is explored empirically. Laboratory measurements have been made over deterministic random arrays of identical varnished wooden semi-cylinders on a glass plate. The agreement between predictions and measured relative sound pressure level spectra is very good both for single deterministic random distributions and for averages representing non-deterministic random distributions. The analytical theory is found to give identical results to a boundary element calculation but is much faster to compute.