FeSi may be one of the main products of the reaction between molten iron and mantle silicates. We use both the Local Density Approximation (LDA) and the Generalized Gradient Approximation (GGA) to Density Functional Theory (DFT) to analyze the structural behavior of FeSi and to determine its elastic properties up to high pressures. According to our calculations, at lowermost mantle pressure conditions, FeSi is in the B2 (CsCl-type) structure. The B20-B2 transition takes place at 30 GPa in LDA and 40 GPa in GGA and is characterized by a 0.35 g/cm3 shift in density.