Seismic velocity and anisotropy are mainly controlled by the elastic components of rock microstructure. Here we present a MATLAB program, GassDem (Gassmann Differential effective medium), for modeling anisotropic seismic properties from rock microstructure using differential effective medium (DEM) theory and Gassmann's (1951) poroelastic relationship. Modeling provides a method to overcome the limitations of laboratory measurements, which are unable to reach realistic temperature and pressure conditions. DEM models a two-phase composite that consists of a background medium and inclusions. Components of the rock microstructure, such as porosity, crack geometry, and fluid type in the cracks, are considered to be inclusion properties in DEM theory. Gassmann's poroelastic relationship is used to calculate the elastic stiffness for fluid-saturated rocks. In the formulation of the DEM model, we achieve high numerical efficiency, particularly for inclusions with large aspect ratios, by taking the Fourier transform of the tensor Green's function and using the symmetry of the tri-axial ellipsoid to reduce the amount of integration. We provide examples of DEM modeling and a description for users to replicate the examples using the GassDem graphical user interface, or using a MATLAB script.