A hyperbolic equation is considered for the propagation of pressure disturbance waves in layered fluids having different fluid properties. For acoustic problems of this sort, the characteristic finite element model alone does not suffice to ensure prediction of the monotonic wave profile across fluids having different properties. A flux corrected transport solution algorithm is intended for incorporation into the underlying Taylor–Galerkin finite element framework. The advantage of this finite element approach, in addition to permitting oscillation-free solutions, is that it avoids the necessity of dealing with medium discontinuity. As an analysis tool, the proposed monotonic finite element model has been intensively verified through problems which are amenable to analytic solutions. In modeling wave propagation in layered fluids, we have investigated the influence of the degree of medium change on the finite element solutions. Also, different finite element solutions are considered to show the superiority of using the flux corrected transport Taylor–Galerkin finite element model.