This paper presents an efficient algorithm, FDA2DMT (Free Decay Analysis for 2D Magnetotellurics (MT)), based on eigenmode approach to solve the relevant partial differential equation, for forward computation of two-dimensional (2D) responses. The main advantage of this approach lies in the fact that only a small subset of eigenvalues and corresponding eigenvectors are required for satisfactory results. This small subset (pre-specified number) of eigenmodes are obtained using shift and invert implementation of Implicitly Restarted Lanczos Method (IRLM). It has been established by experimentation that only 15–20% smallest eigenvalue and corresponding eigenvectors are sufficient to secure the acceptable accuracy. Once the single frequency response is computed using eigenmode approach, the responses for subsequent frequencies can be obtained in negligible time. Experiment design results for validation of FDA2DMT are presented by considering two synthetic models from COMMEMI report, Brewitt-Taylor and Weaver (1976) model and a field data based model from Garhwal Himalaya.