We investigate numerical schemes for solving 3D paraxial wave equations that are compatible with the use of splitting methods without losing accuracy. The novelty of these paraxial equations (introduced in \cite{col.jol:2}) compared with classical alternate directions methods is to use more than the two usual cross-line and in-line directions for the splitting. It gives rise to a series of 2D extrapolations in each direction of splitting. Propagation along depth is done with a higher-order method based on a conservative Runge Kutta method. The discretization along the lateral variable is done using higher-order finite difference variational schemes. We present a detailed plane wave analysis in a homogeneous medium that leads to a classification of several particular schemes with respect to the numerical dispersion they generate. The dispersion an= alysis extended to 3D helps chosing the «best» coefficients of the extrapolati= on operators on the dispersion point of view. We conclude with numerical experiments in 2D as well as in 3D homogeneous and heterogeneous media.