We examine the effect of a dynamic stress on the reduction of flow in porous media using polymer gels formed in situ. To develop the theory for the response of the gel, we consider three dominant factors: (a) compressive (elastic) deformation of the gel and porous medium, (b) microscopic flow in this system, and (c) gel displacement. The latter occurs when the stress p is larger than a certain critical value pc, satisfying pcR2=constant (R=effective pore radius), where the constant is an increasing function of elastic modulus of the gel and its cross-linking energy. The expulsion of the gel above pc is reminiscent of growing Saffman-Taylor instabilities. To derive analytic expressions for the macroscopic saturation profiles we use the formalism for fully miscible two-phase flow. The equation of evolution of the pressure, established by mass balance arguments, was solved analytically. For p<pc, the pressure obeys an exponential saturation function while for p<pc, it first increases, reaches a maximum value, and then decreases towards an asymptotic value. These theoretical predictions are supported by our experiments consisting of injecting (salt) water at a constant flow rate in porous samples containing a organically cross-linked polymer gel (co-polymer of acrylamide and t-butyl-acrylate cross-linked using poly-ethylene-imine). The data confirms further that the product pcR2 is constant and prove that both pc and the maximum pressures increase with intrinsic gel strength.