OICC Press Journal of Solid Mechanics 2008-7683 6 4 2014 09 30 Implementing the New First and Second Differentiation of a General Yield Surface in Explicit and Implicit Rate-Independent Plasticity 310 321 EN F Moayyedian Mechanical Engineering Department, Ferdowsi University of Mashhad M Kadkhodayan Mechanical Engineering Department, Ferdowsi University of Mashhad Journal Article 2014 09 30 In the current research with novel first and second differentiations of a yield function, Euler forward along with Euler backward with its consistent elastic-plastic modulus are newly implemented in finite element program in rate-independent plasticity. An elastic-plastic internally pressurized thick walled cylinder is analyzed with four famous criteria including both pressure dependent and independent. The obtained results are in good agreement with experimental results. The consistent/continuum elastic-plastic moduli for Euler backward method are also investigated.