The principal soil gases of current concern to building are radon and landfill gas. The flow of these is generally considered to be dominated by viscous flow driven by pressure differences. This paper presents results for the pressure-driven flow of gas for problems relating to a building with a bare soil floor, for example below a suspended timber floor. This paper builds on a previous paper by mapping the solution to a mixed boundary problem onto another geometry. In a third paper these results will be compared with an analytical result from elsewhere and an experiment.