Simulations of the interaction of very intense short pulse lasers with solid density plasmas have indicated that there may be very high magnetic fields and electron temperatures in the vicinity of the focal spot. We investigate the propagation of an incident electromagnetic wave under these conditions, both analytically and by means of a particle code, and show that the evanescence length of the wave field in a highly overdense plasma may be much greater than is usually supposed. This effect could be important in understanding the penetration of energy into the overdense region and the particle heating and acceleration which takes place there.