Abstract: A set of new formulas for the precise determination of critical diameter of thermal insulation for cylinders and spheres is derived under the condition of simultaneous heat losses by convection and by radiation.Convective and radiative coefficients of heat transfer are treated separately to take care of their difference on their laws of edpendency to diameter and to temperature duop.A convenient graphical method of practical evaluation is presented.In the concluding part of this paper,some interesting particular cases are discussed.