Before revision: We show that the Fr\'echet distance of two-dimensional parametrised surfaces in a metric space is computable . This settles a long-standing open question in computational geometry .
After revision: We show that the Fr\'echet distance of two-dimensional parametrised surfaces in a metric space is computable in the bit-model of real computation. An analogous result in the real RAM model for piecewise-linear surfaces has recently been obtained by Nayyeri and Xu (2016) .