Arbitrary Lagrangian Eulerian (ALE) finite element method is extensively used for numerical simulation of solid mechanics problem. The versatility of the mesh in ALE approach makes it particularly effective and efficient in solving large deformation problems. In this work, a complete treatment of fully coupled ALE formulation is presented incorporating inertial, rate and thermal effects. The formulation may be used in conjunction with thermo-elasto-viscoplactic material models. A consistent and efficient tangent operator is developed in closed form to handle stress integration. The applications of this formulation are given in the second part of this paper.