There are many materials that have different moduli in tension and compression. The properties of such dimodular materials can be described with the aid of a potential that depends on the first and second invariants of the stress tensor. The potential for the classical elastic body is a special case of this. A method for determining the functions and the constants in the expression for the potential is described. Possible forms of the stress-strain diagrams under proportional and nonproportional loading are discussed. Finally, the validity of certain theorems of the theory of elasticity in the case of dimodular materials is analyzed.