A new formulation called the slowly varying method (SVM) is proposed in this paper to solve high‐frequency scalar scattering problems. It is well known in linear acoustics that, excited by a plane harmonic incident waveU0(x) impinging on a scatterer, the scattered fieldU(x) for a Neumann boundary value problem or ∂U(x)/∂nfor a Dirichlet boundary value problem is quickly varying on a scatterer whenka≫1, wherekis the wave number andais a typical scatterer dimension. The paper shows that for the samekathe functionV(x)=U*0(x)U(x) for the Neumann boundary condition andVn(x)=U*0(x)∂U(x)/∂nfor the Dirichlet boundary condition exhibit much slower variations on the scatterer compared with those ofU(x) and ∂U(x)/∂nfor some cases. Here,U*0(x) is the complex conjugate ofU0(x). The relations amongV(x),Vn(x) and the acoustic energy densities have been analyzed. A new boundary integral equation in terms of the unknown functionV(x) orVn(x) on the scatterer may be derived. This boundary integral equation can be either solved by the BEM or asymptotically simplified by the stationary phase method and other approximations. For the former case, the requirement that the boundary element dimension should be proportional to 1/(ka) may be waived for obtaining satisfactory numerical results. For the latter case, a non‐element numerical solution ofV(x) orVn(x) then may be obtained by an algebraic arithmetic without solving large‐dimensional linear‐algebraic equations. A few numerical results obtained by the SVM are presented in the paper as well as their comparison with the conventional BEM solutions.