The solar chimney power plant uses solar radiation to raise the temperature of the air and the buoyancy of warm air to accelerate the air stream flowing through the system. Conventionally, solar chimney power plants need a very large flat land area for the installation of a very large relatively-horizontal collector system. There is also the proposal to construct solar chimneys in sloped lands that have the acceptable solar-heat-flux level. To do that, the collector of a solar chimney system must be sloped. In this study, a mathematical model of solar chimney power plants with sloped collector was developed. The solar collector, chimney and turbine were modeled together theoretically, and iteration techniques were then carried out to solve the mathematical model. Very good agreement was found between mathematical results and commercial software code predictions. The power output of the system is estimated and compared with the prediction from the literature. The results show that the prediction from the literature is underestimated.