The near‐field scattering of plane waves by a submerged thin elastic cylindrical shell witnesses a shadow boundary generated by thegeometricalacoustics field, which is not encountered in the far field except in the immediate vicinity of the forward scattering direction. Even in the lit zone, the incident and reflected rays may appear close and are not well separated. Based on these physical observations a modified ray acoustic approach is proposed here that combines the two spectral integrals that would give rise to separate incident and reflected fields when reduced by saddle point evaluation. The resulting single integral descriptive of the geometrical acoustics field can be cast as an integral version of the harmonic series form for the total (incident plus scattered) field, thereby facilitating its numerical computation. Averting the asymptotic integration procedure, and hence the contour deformation involving possible capture of the membrane wave poles, the new algorithm predicts the total near field uniformly over theentireazimuthal domain, which is now synthesized by the geometrical acoustics field and the shell‐guided phase‐matched compressional and shear wave field. Extensive numerical examples for the field dependency on frequency as well as on azimuthal and aspect angles are presented; they indicate that the modified ray acoustic solution leads to remarkable accuracy forka≥1 or so (wherekis the fluid acoustic wave number andais the shell mean radius). By reciprocity, the method presented in this paper applies as well to excitation by an axially phased line source located atfinitedistance (on‐ or off‐surface).