In this paper we consider high frequency properties of composite materials. We use Monte Carlo simulations and Effective Medium Theory (EMT) to calculate the dielectric constant and the magnetic permeability. The EMT is a well-known approximation which is used for describing the conductivity, dielectric constant, and magnetic permeability of granular materials consisting of conducting and nonconducting components. Different modifications of this theory are considered when the skin layer depth is larger then the characteristic size of the conducting inclusions. In the microwave range it is necessary to take into account the internal inductance of the materials and presence of strong skin effect in conducting granules. In this paper we calculate the internal inductance of materials using a Monte Carlo simulation and then derive EMT equations in the presence of skin effects and the internal inductance. We obtain the dielectric constant for the materials with different shapes of conducting inclusions (spheres and sticks). The frequency dependence of the effective dielectric constant for the materials with conducting sticks is substantially different from those known earlier for composite materials. The theoretical results are in agreement with experimental results for the microwave dielectric constant of the polymer composites containing carbon fibers.