Hot isostatic pressing (HIP) combines high temperatures and pressures to consolidate powder metals (PM) to form exotic parts that cannot be obtained from traditional manufacturing processes. Manufacturers need to utilize mathematical tools, such as the finite element (FE) method, to simulate the HIP process to avoid the trial and error method in product and process development. FE simulations of the HIP process require constitutive models that simultaneously capture the various deformation mechanisms, such as plasticity and creep, during powder densification. Since the HIP process can occur over several hours, these numerical implementations need to be both accurate and efficient for manufacturers to exploit the HIP process fully. This paper presents a new and efficient numerical scheme that accelerates FE calculations of PM that undergoes the HIP process. This work couples the constitutive models presented in Van Nguyen et al. (2017) for thermal, creep, plasticity, and density changes into a seamless integration scheme. The proposed numerical scheme is implemented a user-defined material subroutine (UMAT) for mechanical calculations in an implicit formulation of the commercial finite element software LS-DYNA. A thermal user-defined material subroutine (ThuMAT) is also implemented to account for the porosity effect on thermal properties in thermal calculations. FE simulations of a stainless steel 304/316 L capsule that undergo the HIP process are performed to highlight the efficiency of the proposed model. The predicted deformed shape of the capsule using the proposed integration scheme showed excellent agreement with previous implementations. Furthermore, the proposed integration scheme can provide a computational speedup of up to 1,100% without a loss of accuracy compared to previous implementations.