Transparent insulation materials (TIMs) can combine the advantages of opaque insulation with solar collection when applied to building facades. Mathematical models developed to calculate the optical performance of a transparent insulated (TI) system are presented. The TI-system modelled consisted of a 6 mm outer glass pane, a 22 mm wide polymethylmethacrylate (PMMA) capillary cell section and an 8 mm inner glass pane. When solar beam radiation passed through the TI-system, the solar transmittance, absorptance and reflectance that occurred in the system were calculated. Optical interactions at each layer in the TI-system were numerically modelled for five incidence angles. A direct to diffuse transmittance was calculated for solar radiation passing through the PMMA capillary cells with an incidence angle, theta(i), in excess of 0 degrees. The calculated transmittance for the PMMA capillary cells at 0 degrees incidence angle was 0.8264 with overall solar transmittance of up to 0.66 calculated for the whole TI-system, a value which is consistent with that found in previous research. This paper presents a method for calculating the optical properties for multiple PMMA capillary cells, encapsulated between two glass panes for different solar incidence angles, with input of relevant data from other sources. This method can also be adapted for other types of glazing systems. (C) 2014 Elsevier Ltd. All rights reserved.