An algorithm for accurate three‐dimensional ray tracing is presented for realistic, nonspherical ionospheric electron density distributions, ignoring effects of the magnetic field. At the start of each ray path increment a truncated Taylor series expansion of the electron density results in a computationally efficient, closed‐form solution of the Euler‐Lagrange equations for the increment. The technique is applied to computations of ray paths in a nonspherical ionosphere which is specified by a climatological model used for HF over‐the‐horizon (OTH) radar studies. The effects of tilts in a sunrise transition region on signal losses and ray path deviations are found to be substantial. Results of various ionospheric approximations used for single‐site transmitter location are calculated.