The object of this study is to evaluate the performance of the finite element variational multiscale stabilized method combined with local preconditioning for the solution of the Euler equations for steady problems. Local preconditioning is applied to the Euler equations for compressible steady flow. These equations are solved using the finite element method. A variational multiscale stabilization for the Euler locally preconditioned equations is proposed and applied to problems covering a large range of Mach numbers, from low Mach to supersonic regimes. van Leer-Lee-Roe’s and Choi-Merkle’s preconditioners are applied to the Euler equations and the results are compared to the ones obtained without preconditioning, in terms of convergence and accuracy of the solution.