The elastic constants that control P- and SV-wave propagation in a transversely isotropic media can be estimated by using P- and SV-wave traveltimes from either crosswell or VSP geometries. The procedure consists of two steps. First, elliptical velocity models are used to fit the traveltimes near one axis. The result is four elliptical parameters that represent direct and normal moveout velocities near the chosen axis for P-and SV-waves. Second, the elliptical parameters are used to solve a system of four equations and four unknown elastic constants. The system of equations is solved analytically, yielding simple expressions for the elastic constants as a function of direct- and normal-moveout velocities. For SH-waves, the estimation of the corresponding elastic constants is easier because the phase velocity is already elliptical. The procedure, introduced for homogeneous media, is generalized to heterogeneous media by using tomographic techniques.