In this paper, the behavior of free vibrations and buckling of the sandwich panel with a flexible core was investigated using a new improved ‎high-order sandwich panel theory. In this theory, equations of motion were formulated based on shear stresses in the core. First-order shear deformation theory was ‎applied for the procedures. In this theory, for the first time, incompatibility problem of velocity and acceleration field existing in Frostig's ‎first theory was solved using a simple analytical method. The main advantage of this theory is its simplicity and less number of equations than the ‎second method of Frostig's high-order theory. To extract dynamic equations of the core, three-dimensional elasticity theory was utilized. ‎Also, to extract the dynamic equations governing the whole system, Hamilton's principle was used. In the analysis of free vibrations, the ‎panel underwent primary pressure plate forces. Results demonstrated that, as plate pre-loads got closer to the critical buckling loads, the natural frequency of the panel tended zero. The results obtained from the present theory were in good correspondence with the ‎results of the most recent papers. تفاصيل المقالة