The main differentiating point between the meshfree and finite element methods is the shape function. The paper is intended to elaborate the construction of the moving least square approximation shape function and their derivatives in one-dimension, by presenting the related plots of shape function and its derivatives; with different parameters. A tapered bar subjected to tensile load using the element free galerkin method, applying the moving least square approximation shape function, has been modeled and tip displacement with exact and meshfree solution has been found to be in good agreement.