A numerical method is presented for calculating the sound pressure around a noise barrier of constant but arbitrary cross-section. To obtain the exact solution of this problem, the Helmholtz equation must be solved in the three-dimensional domain outside the barrier. It is shown in this article how to calculate this 3-D sound pressure from solutions of simpler problems defined on the two-dimensional domain outside a cross-section of the barrier. The numerical solution of a large three-dimensional problem is thus avoided and the efficiency of the calculation is considerably improved especially when a whole frequency spectrum is needed. By using the boundary element method to calculate the numerical solutions in the two-dimensional domains, examples are given of determinations of sound pressure fields created by a point source and by an incoherent line source. In this way the efficiency of barriers of different cross-sections can be compared by using the real sound pressure around them. From the frequency spectrum at a point, one can then calculate by Fourier transform the temporal variations of the sound pressure created by a noise source moving in a direction parallel to the barrier.