The effect of boundary conditions on the solution of the inverse problem of identifying the geometry and location of a cavity inside an elastic solid body using displacement measurements obtained from a tension test is investigated. The boundary elements method (BEM) coupled with the genetic algorithm (GA) and the conjugate gradient method (CGM) are implemented in this identification problem. A fitness function which is defined as the squared differences between the computed and measured displacements is minimized. The best initial guess of the unknown shape and location of the cavity is found by the GA, then this initial guess is used by the CGM to achieve convergence. The imposed boundary conditions, i.e. geometrical constrain and specified tractions are kept constant during all iterations. Certainly changes in the boundary conditions can be effective in the correct identification of the shape and location of the cavity. In this study the effect of different boundary conditions on the convergence is investigated and the best and the most suitable boundary conditions which results in the faster and more accurate convergence are found.