The paper describes a method for the arch dam analysis, capable of handling arch dams of arbitrary geometry. The median surface of the structure is divided into three-dimensional elements by a nonorthogonal computational mesh. For the general case there are formulated the strain - displacement relationships, the equilibrium equations in terms of the mechanical and thermal loads and the proper boundary conditions. The numerical integration, using the finite difference procedure, leads to a set of n linear equations with n unknowns. The capabilities of the new method are shown by the application to the analysis of the Tarnita dam (H(maximum) equals 96 m), recently completed in Rumania.