This chapter discusses a custom quadrature scheme for the MLS shape functions to ensure the properties needed for exact verification of the patch test. In the “patch test”, a linear elasticity problem must be exactly solved when the solution is a linear function. The obtained strains and stresses should be constant. When a numerical method of solving the partial differential equations fulfills this condition, it is said to pass the “patch test.” This approach to test the numerical formulation and the code itself is standard in the finite element method. The MLS shape functions do not have the polynomial form. Therefore, the integration is not well performed by the classical Gauss–Legendre scheme.