Slope discontinuities and T-sections can be modeled in a straight forward manner using fully parameterized absolute nodal coordinate formulation (ANCF) finite elements that have a complete set of gradient vectors. Linear transformations that define the element connectivity can always be obtained and used to preserve ANCF desirable features that include constant mass matrix and zero Coriolis and centrifugal forces in the case of spinning structures. The objective of this paper is to develop a general method that allows for modeling slope discontinuities and T-sections using gradient deficient ANCF finite elements that do not have a complete set of coordinate lines and gradient vectors. Linear connectivity conditions that preserve all the ANCF desirable features including the constant mass matrix are developed at the nodes of slope discontinuities. At these nodes of discontinuity, one can always define a complete set of independent coordinate lines that lie on the structure. These coordinate lines can be used to define a complete set of independent gradient vectors at these nodes. Since the proposed method is based on linear coordinate transformations, the method can be implemented in a preprocessor computer program. The application of the proposed general method is demonstrated using ANCF gradient deficient beam element example.