Summary: Mesh matching discussed in this paper refers to a situation when two adjacent lines or surfaces with different meshes on them joint together. A mesh matching formulation is given by enforcing sticking conditions on the jointed lines and surfaces. The preservation of uniform displacements (stress distributions) across the matched meshes is investigated. This, in the contact context, is usually called patch test. The conditions to ensure the formulation pass the patch test are derived, that include partition of unity and compatible conditions of shape functions, as well as the inf-sup condition of the augmented equilibrium equations. The proposed formulation is a general one from which some special cases, such as one-pass and two-pass node-to-surface contact procedures, can be recovered. Various examples are given to show the patch test performances of lower and higher-order mesh matching (contact) formulations for both straight and curved inter faces in 1-D. For a general 2-D problem, an example demonstrates that, unlike its behaviours in 1-D, two-pass node-to-surface contact procedure using linear elements could not pass the patch test.