IsoGeometric Analysis (IGA) is adopted for solving the Boundary Integral Equation (BIE), associated with the Neumann-Kelvin problem, calculating the wave resistance of ships advancing with constant forward speed on the free surface of an ideal (inviscid, incompressible, irrotational) fluid. In contrast with low-order panel methods, where body geometry is approximated by a large number of quadrilateral panels on which the velocity potential is assumed to be piecewise constant (or approximated by low degree polynomials), the IGA concept is based on exploiting the NURBS basis, used for representing exactly the body geometry, for approximating the unknown singularity distribution involved in the BIE. The accuracy of the developed IGA-based Boundary Element Method is examined by comparing the numerical results obtained for submerged and surface piercing bodies against analytical solutions, experimental data and predictions provided by the low-order panel or other similar methods appeared in the pertinent literature, demonstrating also the superior efficiency of the isogeometric approach.