Cylindrical and Spherical problem in Mechanical engineering has been discuss by using Seth's B.R. Theory.For the problems in Elastic - plastic transition stresses in a transversely isotropic thick-walled cylinder subjected to internal pressure and steady state temperature, it has been observed that at room temperature, thick-walled cylinder made of isotropic material yields at a high pressure at the internal surface as compared to cylinder made of transversely isotropic material. With the introduction of thermal effects isotropic/transversely isotropic cylinder yields at a lower pressure whereas cylinder made of isotropic material requires less percentage increase in pressure to become fully-plastic from its initial yielding as compared to cylinder made of transversely isotropic material.And for the Problems Elastic - Plastic Transition Stresses in a Spherical Shell under internal Pressure by using concept of Lebesgue measure, it has been seen that the result are same as given by Mellor, Hill and Seth's.