Shape dynamics possesses the same dynamics as general relativity, but has different gauge orbits. The link between general relativity and shape dynamics can be established using the ADM formalism in the following way: Shape dynamics can be gauge fixed in such a way that its initial value problem and its equations of motion coincide with the initial value problem and equations of motion of the ADM formalism in constant mean extrinsic curvature gauge. This equivalence ensures that classical shape dynamics and classical general relativity are locally indistinguishable. However, there is the possibility for global differences.