An MHD unsteady one-dimensional model is used to simulate the interaction and coalescence of two pressure waves in the outer heliosphere. Each of the two pressure waves was a compression region bounded by a shock pair. Computer simulation using Voyager data as input demonstrates the interaction and coalescence process involving one pressure wave associated with a fast stream and the other pressure wave without a fast stream. The process predicts a significant change in the magnetic field and plasma signatures: The propagation of the forward and reverse shocks first widens the radial dimension of the shock compression region with increasing heliocentric distances. The shocks belonging to two neighboring compression regions eventually collide, and the two compression regions begin to overlap. Both shocks continue to propagate after the collision, but they are weakened. As a result of the collision, a contact surface is formed in the overlapping compression region. The magnetic field, plasma density, and temperature in the new compression region are enhanced. If this type of interaction is a dominant dynamical process in the outer heliosphere, it can significantly and irreversibly alter the structure of the medium.