Among the Lattice Boltzmann (LB) methods the entropic variant, called Entropic Lattice Boltzmann Method (ELBM) has become popular in solving compressible flows. This model requires no different formulations for isothermal, multiphase or compressible flows. The fundamental logic behind the method is the expansion of double equilibrium distribution functions under entropy constraints as well as using higher-order multi-speed lattices and dividing the collision process into two parts consisting of a quasi-equilibrium state [1]. ELBM is an inherently transient and explicit calculation method. This paper provides a short description of the method in terms of the core principles, mathematical framework, followed by a three-dimensional (3D) implementation of it. Particular focus is directed toward the efficient solution of its relaxation parameter that satisfies an entropy constraint for stability. The results of a few 3D validation cases, including supersonic flow around a sphere, are presented to assess the effects of the relaxation parameter calculation procedures as well as demonstrate the capabilities of the method.