Differential Quadrature (DQ) is an efficient derivative approximation technique but it requires a regular domain with uniformly arranged nodes. This restricts its application for a regular domain only discretized by the field nodes in a fixed pattern. In the presented random differential quadrature (RDQ) method however this restriction of the DQ method is removed and its applicability is extended for a regular domain discretized by randomly distributed field nodes and for an irregular domain discretized by uniform or randomly distributed field nodes. The consistency analysis of the locally applied DQ method is carried out, based on it approaches are suggested to obtain the fast convergence of function value by the RDQ method. The convergence studies are carried out by solving 1D, 2D and elasticity problems and it is concluded that the RDQ method can effectively handle regular as well as irregular domains discretized by random or uniformly distributed field nodes.