In this paper we introduce a new element called solenoidal edge element for the finite element method. This element is specially designed for electromagnetic modeling. The basis functions are chosen to automatically satisfy the wave equation within each element. The main advantage of such elements is that they have very low numerical dispersion relative to more commonly used nodal and edge elements based on polynomial approximations. The accuracy of the elements is demonstrated, for boundary value, eigenvalue, and scattering problems. ¿ American Geophysical Union 1996