A new technique for analysing problems which extend to infinity using elements is presented. A typical situation is that of the unbounded surface wave problems, either in two or three dimensions. The strategy is to discretize the inner domain in the standard finite element manner and to discretize the outer domain which extends to infinity with special infinite elements, for these elements are here suggested a series of shape functions analogous to Lagrange polynomials, but including an exponential decay. These shape functions are applied to an illustrative example which shows the success of the method.