Many underwater‐acoustics propagation problems are solved using geometrical acoustics. This approach uses an approximate formulation of the wave equation which is exact in the limit of infinite frequency. The computation of the ray paths and the associated intensities involve the use of four first‐order nonlinear ordinary differential equations. In order to have smooth, continuous solutions, the velocity field (i.e., the speed of sound field) and its derivatives, which appear in the coefficients of the set of differential equations, must be twice continuously differentiable (C2) throughout the region. The use of splines—cubic polynomials which are continuous through the second derivative—insures compliance to these requirements. This paper gives a technique for calculating a spline field in two dimensions, given data points which are available at specific ranges, but at different depths. The technique is easily extendable to include arbitrary location of data points. This use of splines, in order to provide a smooth function for use in differential equation‐solvers found so often in computer algorithms, should be of utility in various fields.