This book is a detailed treatment of volume and surface force-densities and mechanical stresses in electrically and/or magnetically polarized bodies. The classical approach applies equally well to the electric and/or to the magnetic case. The issue of computation of force densities in materials is still a controversial one, but it is very important in many practical applications. These include the design of electric machines and various power apparatus, permanent magnet devices, and piezo-electric actuators and sensors. By combining electrodynamic theory, continuum mechanics and classical thermodynamics, important and reliable formulas for force densities are derived and settled. In particular, the well-known controversy between the Helmholtz and the Kelvin formulas for force densities in linear fluid dielectrics is analyzed in detail in the light of existing experimental results.