A new differential formulation is presented for acoustic wave scattering from rotationally symmetric penetrable bodies. The numerical implementation of this formulation is fairly simple, and comprises basically the construction of the state‐transition matrix of a system of differential equations and the solution of a matrix equation. The validity and the accuracy of the numerical scheme are tested considering objects of known scattering behavior. Other numerical applications are also presented to demonstrate the generality of the method in handling scatterers of arbitrary shapes and material compositions.