To solve crack problems, some coupled methods have been developed in recent years. Most of these methods have some shortcomings such as the need for a transition region. The finite element and enriched element free Galerkin methods are widely used for this class of problems. In order to take the advantages of these methods while avoiding the disadvantages, it is essential to follow solution approaches based on a combination of them. Prompted by this idea, in this article, the authors mainly aim at finding a simple way to solve the problem of a cracked plate by using a novel coupled finite element-element free Galerkin (FE-EFG) method. In this procedure, the usage of transition region is bypassed by employing the concept of andldquo;virtual particlesandrdquo;. The enriched element free Galerkin method is applied to approximate regions near a crack tip and the finite element method is put to use in the areas far from the crack tip. Static analysis of two-dimensional crack problems, according to the plane stress condition under mode-I loading, has been done. The results from the present method are indicated to be in excellent agreement with those from the existing analytical solutions.