A shape preserving surface interpolation scheme to data set without three consecutive collinear data points in both x and y directions is presented, which is a piecewise quadratic parametric polynomials, and is G1 or C1 continuous as desired on the whole domain. The interpolating surface can preserve the convexity, concavity, inflection property and monotonicity of the data set. Futhermore, some parameters (such as the cross boundary tangent vectors of the adjacent sub-surfaces) can be freely chosen within a certain extent to adjust the shape of the interpolating surface or to obtain a better approximation to the original function from which the data come. The shape preserving interpolation to an arbitrary set of data on rectangular grids is also discussed, and an algorithm with generality is described, a special case of which is the algorithm of the above G1 (or C1) shape preserving interpolant. A number of examples of the algorithmsare given.