Starting from regular domains described in principal curvilinear coordinates, a completely arbitrary shape is obtained by means of Non-Uniform Rational B-Splines (NURBS) due to the advantages shown in the well-known isogeometric analysis (IGA). The mapping technique based on the use of blending functions is illustrated to twist the original domain into the distorted one without subdividing the reference domain into sub-elements or finite element (FE). The procedure is extremely general and allows to deal with different boundary condition combinations and stacking sequences. Its validity is proven by the comparison with the results available in the literature concerning arbitrarily shaped plates or obtained through three-dimensional FE models.