A model to describe a solar chimney power plant with a generally sloped collector field and for the general situation of humid air is presented. This is a significant development of existing simple models for solar updraft towers with planar collector fields for the sit- uation of purely dry air. The model describing the gas dynamics in the collector and in the chimney includes a turbine model, friction and heat transfer losses, evaporation and condensation models etc. However, the relevant physics can be modeled in one space di- mension. It is the result of a fully compressible gas dynamic model in the small Mach number limit. A numerical algorithm is defined which admits very fast simulations. There- fore optimization procedures can easily be applied. Numerical results on optimization with respect to geometric and physical parameters which may be considered both in the plan- ning and the operational phase are presented. The results are compared qualitatively and ���if available ���quantitatively to prototype data and to simulations from the literature.