Exact solutions for the one-dimensional problem of a compressible fluid having a time-dependent pressure at the source (fracture face) and displacing a compressible reservoir fluid are generated. Special solutions for various cases represented by step, step with constant slope front, and sinusoidal pressure variations at the fracture face are derived. Numerical results and trends for fluid interface motion are revealed for selected cases. The applicability of the presented solutions to hydraulic fracturing is discussed. In addition, response solutions for problems in reservoir mechanics, underground coal gasification, and nuclear waste management can be similarly investigated.