The generalized self-consistent method (GSCM) in conjunction with a computational finite element method is used to calculate the anisotropic effective moduli of a medium containing damage consisting of microcracks with an arbitrary degree of alignment. Since cracks respond differently under different external loads, the moduli of the medium subjected to tension, compression and an initially stress-free state are evaluated and shown to be significantly different, which will further affect the wave speed inside the damaged media. There are four independent material moduli for a 2-D plane stress orthotropic medium in tension or compression, and seven independent material moduli for a 2-D plane stress orthotropic cracked medium, which is initially stress free. When friction exists, it further changes the effective moduli. Numerical methods are used to take into account crack face contact and friction. The wave slowness profiles for microcrack damaged media are plotted using the predicted effective material moduli.