An alternative formulation of the Helmholtz integral equation, derived by Wu et al. [J. Acoust. Soc. Am. 103, 1763-1774(1998)], expresses the pressure field explicitly in terms of the velocity vector of a radiating surface. This formulation, derived for arbitrary sources, is similar in form to Rayleigh's formula for planar sources. Because the pressure field is expressed explicitly as a surface integral of the particle velocity, which can be implemented numerically using standard Gaussian quadratures, there is no need to use the boundary element method to solve a set of simultaneous equations for the surface pressure at the discretized nodes. Furthermore the nonuniqueness problem inherent in methods based on Helmholtz integral equation is avoided. Validation of this formulation is demonstrated first for some simple geometries. This method is also applied to general vibro-acoustic problems in which both the surface pressure and velocity components are unknown.