Fast and accurate ray tracing in heterogeneous isotropic media is required in many applications of seismology. We propose two analytical techniques of perturbation, the ''variation of coordinates'' method and the ''variation of constants'' method, which are faster than an entirely numerical procedure. From a local polynomial expansion of the square of slowness, we explicitly write perturbed analytical expressions for rays, paraxial rays, polarization vectors and travel times. These expressions are in a form suitable for computer programming. Based on these expressions, a finite element approach is proposed where the medium is divided in rectangles for two-dimensional media and in parallelepipeds for three-dimensional media. The ''variation of coordinates'' method is well adapted for cardinal b spline interpolations of the square of slowness in each cell. We have found that b splines of order 4 give a good compromise between the number of elements for describing the heterogeneity of the medium and the efficiency of computing perturbed analytical expressions for rays in each element. ¿1991 American Geophysical Union