Two methods of computing interval velocities from offset vertical seismic profiles are developed based on a horizontally layered earth model. The first method is a simple iteration procedure by which layer velocities are sequentially computed. For any given layer, the take-off angle for the ray arriving at the geophone at the bottom of the layer is varied until the velocity computed from travel time differs from the velocity obtained from Snell's law by less than some specified value. This is similar to the ''shooting method'' in ray tracing. This method requires as many layers as geophone locations. The second method is more general, and the only requirements are that the number of layers be equal to or smaller than the number of geophone locations and that the rays arrive at the geophones from above. This method is based on the iterative solution of a linearized problem obtained by expanding travel times and horizontal distances in Taylor series as functions of velocities and p-parameters up to first order in dv's and dp's (perturbations in velocities and p-parameters, respectively) and assuming initial estimats v0's and p0's close to the optimum solution. The resulting linear system is solved using a simplified version of the Levenberg-Marquardt algorithm. Due to the simple structure of the ensuing matrix of derivatives, for each iteration the problem reduces to the solution of an inverse problem for the velocities alone plus the solution of a vector equation for the p-parameters. This method is fast, and convergence is attained even in the case of poor initial estimates.