An analytic solution is presented to the problem of transient flow to a partially penetrating well that is open in either layer of finite thickness in a two-layered system. Crossflow is permitted at the interface between the two layers. Closed form solutions have been obtained which can easily be evaluated numerically. Simplified forms of the solutions for small and large values of time have been developed from the main solution. It has also been shown that the solution reduces to the case of single layer partial penetration once we allow the permeability of the nonperforated layer to vanish. The approach here is to start with the problem when the pumping well is open only in the top layer. A second solution is also developed when the well is partially penetrating only in the lower layer; LBL-9479