Summary: This paper studies a class of nonconforming spline collocation methods for solving elliptic partial differential equations in an irregular region with either triangular or quadrilateral partition. In the methods, classical Gaussian points are used as matching points and the special quadrature points in a triangle or quadrilateral element are used as collocation points. The solution and its normal derivative are imposed to be continuous at the marching points. We present theoretically the existence and uniqueness of the numerical solution as well as the optimal error estimate in \(H^1\)-norm for a spline collocation method with rectangular elements. Numerical results confirm our theoretical analysis and illustrate the high-order accuracy and some superconvergence features of methods. Finally we apply the methods for solving two physical problems in compressible flow and linear elasticity, respectively.