The singularity-free workspace of parallel mechanisms is highly desirable in a context of robot design. This work focuses on analyzing the effects of the orientation angles on the singularity-free workspace of the Gough–Stewart platform in order to determine the optimal orientation. In any orientation with $\varphi =\theta =0\u2002deg$ and $\psi \u2260\xb190\u2002deg$, the singularity surface becomes a plane coinciding with the base plane. Hence, an analytic algorithm is presented in this work to determine the singularity-free workspace. The results show that the singularity-free workspace in some orientations can be larger than that in the reference orientation with $\varphi =\theta =\psi =0\u2002deg$. However, the global optimal orientation is difficult to determine. Only an approximate optimal orientation is available. The results obtained can be applied to the design or parameter setup of the Gough–Stewart platform.