Coherent anti-Stokes Raman scattering (CARS) microscopy is becoming increasingly popular to characterize biochemical samples. Within this context, we show that theoretical analysis can still be accomplished under the simple assumption of Gaussian volumes instead of spatial shapes obtainable from diffraction necessary to describe the tight-focusing condition realized within the focus of microscopes with high numerical apertures. The assumption, common in other physical and chemical spectroscopic techniques based on microscopy (e.g., fluorescence correlation spectroscopy, photon counting histogram) and never applied to CARS, is here used to determine the expression of the anti-Stokes electric field. Contrary to the standard approach resorting to numerical methods, we find that either the field is analytical for certain shapes of the Raman scatterer or the numerical reconstruction is strongly limited. In addition, we examine tests against two typical problems found in the literature, namely, a description of CARS radiation patterns and CARS imaging. With regard to the latter, we remark that the loss of spatial symmetry, the treatment of which is onerous in standard CARS microscopy because of possible separations between the microscope focus and the Raman scatterer, can be handled with ease in the limit of Gaussian volumes. An example is considered for polystyrene beads that are usually employed as test model of a CARS response of relevant biochemical samples.