  In this paper, we prove the non-uniqueness of stationary solutions to steady
incompressible Euler equations with source terms. Based on the convex
integration scheme developed by De Lellis and Sz\'{e}kelyhidi, the Euler system
is reformulated as a differential inclusion. The key point is to construct the
corresponding plane-wave solutions via high frequency perturbations. Then we
use iteration and Baire category argument to conclude that there exist a large
amount of weak solutions with given energy profile.
