We investigated the nonlinear and nonsymmetric responses of viscoelastic fluids under large amplitude oscillatory squeeze (LAOSQ) flow. The nonlinear and nonsymmetric stress response is a unique feature of oscillatory squeeze (OSQ) flow under larger deformation, but has rarely been investigated. The goal of this study is to systematically characterize the responses of viscoelastic fluids at larger deformation under oscillatory squeeze flow and to provide a platform for the analysis of nonsymmetric stress signals. We report a framework for the analysis of nonlinear-and-nonsymmetric stress signals at larger strain amplitude under oscillatory squeeze flow. The storage and loss modulus showed strain thinning behavior as the strain amplitude increases in both oscillatory shear and oscillatory squeeze flow. However the normal stress under LAOSQ was found to be nonsymmetric in both magnitude and shape unlike the shear stress under oscillatory shear flow. In addition the energy dissipation was found to be larger in extension than in compression. This study is expected to provide a platform to understand the nonlinear and nonsymmetric characteristics of complex fluids under LAOSQ flow.