Pressure-transient solution in a piecewise homogeneous reservoir with arbitrary geometry of each region is proposed by the Laplace domain boundary-element method (BEM). Any number of such regions with different rock and fluid properties can be included in the solution procedure. This formulation can solve for impermeable barriers of any shape, size, and orientation, including large pressure-support sources (aquifers) and fluid-injection problems that show composite behavior. Any number of line-source wells can be included. Example solutions are verified against known analytical solutions. Injection-fluid-front velocity is calculated as part of the solution; thus, the fluid fronts can be tracked in a quasistationary sense. The analytical aspects of this procedure are discussed. BEM solutions are accurate because the method retains the free-space Green's function of the governing differential operator as a global weighting function in the integral equation.