A mesoscale numerical model based on shear transformation zone (STZ) theory is implemented in a commercial finite element software. The model is designed to predict the (visco)plastic deformation response of amorphous solids at the nano- and microscale. The theoretical framework relies on earlier models developed by Bulatov and Argon (1994a) and of Homer and Schuh (2009). We justify the potential of the computational model by conducting reference calculations for model metallic and polymeric glasses in plane strain compression. Emphasis is placed on the effect of time and space discretisation on the predicted macroscopic response. The dependence of the predicted yield strength upon the values of the fundamental model parameters is analysed via a mean-field approximation. The mean-field approximation is validated based on a series of simulations in model parameter space. We provide guidelines for a straightforward but consistent parameter identification method via the mean-field approximation while starting from experimental data.