A ray perturbation formulation for the calculation of rays and travel times in isotropic inhomogeneous media is presented. The ray perturbation theory employed is of first order for the ray deflection and of second order for the travel time. The initial slowness model is parametrized in terms of triangular cells; values are assigned initially to grid nodes and the slowness gradient is assumed to be constant between nodes. The assumption of a constant slowness gradient within a cell leads to a simplification of the ray perturbation equations and a straightforward analytic solution for ray segments in the cells. Imposing boundary conditions that require continuity at cell interfaces leads to a separate tridiagonal system of equations for each component of the ray‐path location vector, which produces an extremely efficient algorithm. The accuracy and speed of this scheme with a 2‐D synthetic crosswell experiment is evaluated. The computation times for the calculations described in this paper depend only on the number of nodes that influence each ray, not the total number of nodes parametrizing the model, so the method promises an even greater increase in speed for 3‐D applications.