Dilational vibration modes have been shown to produce an undesirable “coincidence type” response in the sound‐transmission spectrum of lightweight‐core sandwich panels in the medium to high‐frequency range. In particular, it was found that the dilatational coincidence region often occurs at considerably lower frequencies than those coincidence effects produced by flexural vibration. The governing characteristic frequency equations were developed by employing the Rayleigh‐Ritz Energy Principle for a sandwich panel with variable dimensions and properties. The present solution also employs a general strain energy relation without restricting the skin materials to be identical. Eight characteristic natural frequencies representing dilatational, flexural, and longitudinal vibration were determined for the fundamental as well as higher order modes as a function of panel dimensions and material properties. Throughout this study particular attention was given to the influence of core properties on the dilatational natural frequencies. Experimental panels with various face and core materials were tested under random incidence sound‐transmission conditions and found to compare favorably with the theoretical predictions.