Applying and combining h and p refinement techniques in isogeometric method with the possibility of continuity elevation that this method provides, convergence and error of using different kinds of shape functions with different orders and continuities is investigated. It is done in a numerical analysis framework of a practical and well known problem called “Diametral Compression Test”. The advantage of this case is its circular geometry, since IGA provides designers with high potency of the possibility of using minimum elements to make the exact circular geometry. The point load inserts singularity to the problem. The refinement is utilized uniformly as the effective parameters are limited to the kind, order and continuity of shape functions. With different refinement techniques the convergence of approximated solution to the exact solution of linear elasticity is examined. It is concluded that with the singularity that mentioned, the error in IGA is not necessarily reduced with raise in order, more precisely the level of continuity is another important issue to determine error raise. It is also seen that in the presence of point load singularity the rate of error converges to the same value for all degrees of NURBS and lagrangian shape functions with any continuity. At the beginning of refinement process the minimum number of elements is used to make the process clearer to understand. In next steps h and p techniques and their combination is used to refine the model.