A technique is given to derive the well-known Bell-Szekeres solution of the Einstein-Maxwell vacuum field equations describing the space-time and the Maxwell field following the head-on collision of two homogeneous, plane, electromagnetic shock waves. The analogue of this technique is then utilized to construct the gravitational field following the head-on collision of two homogeneous plane gravitational shock waves. The latter collision, which is followed by a pair of impulsive gravitational waves and a pair of light-like shells traveling away from each other provides a mechanism for generating a cosmological constant.