Belt conveyors, owing to their simple construction, high reliability and relatively low energy consumption, are the basic means of transporting loose and granular materials. Currently, thanks to continuous development, belt conveyors can reach a length of up to several kilometres, and their belt width can be more than two meters. Such possibilities are achieved thanks to increasingly better belts and drives. However, the most common are short belt conveyors with a length of up to 40 m and belt widths of up to 1 m, frequently referred to as belt feeders. Apart from the mining industry, they are widely used in power engineering, metallurgy and other industries (chemical plants, trans-shipment ports, storage yards, etc.). The design of machines, including belt feeders, is based on calculations. Modern design in technology is based on advanced computational methods and the possibilities of computer technology. Multi-variant simulation calculations are necessary, especially in the case of belt feeders, where none of the devices—despite the use of typical elements and subassemblies—are a repeatable solution. Only this procedure guarantees the selection of rational solutions already at the early stages of design. Therefore, in this article, an analytical model of a typical belt feeder was developed and its stability and forces in the supports were determined. This allowed the development of an application for testing the stability of the belt feeder at the design stage or when introducing structural changes.