The authors solve numerically the problem of time-dependent miscible displacement for a finite more-viscous layer confined within a less-viscous layer with width \(W\) in a rectangular domain. The basic equations are continuity equation, Darcy’s law, and the equation of concentration of fluid in the layer, where the dynamic viscosity is assumed to vary exponentially with the concentration. These equations are written in non-dimensional form in terms of streamfunction and vorticity, and are then solved numerically along with prescribed boundary conditions. The Poisson equation for streamfunction is solved by a spectral method with a Galerkin-type discretization of cosine expansion in the streamwise direction, accompanied by a sixth-order compact finite difference scheme in the normal direction. A third-order Runge-Kutta method is used to obtain the temporal concentration distribution. The code is validated by comparing the growth rates with the values obtained from linear stability theory for a plane front with semi-infinite layer, i.e. when \(W\) has an infinite value. Graphs for concentration profile, vorticity and streamfunction patterns are given for different times. The authors find, among other things, that at an earlier time when the influence of finite thickness of the layer is not yet fully realized, the fingers move forward with the features similar to the conventional fingering findings. However, these fingering patterns are redirected upstream after the arrival of most of fingers to the leading front.