Analytical representations of the global potential energy surface of XYn molecules are developed and applied to model the potential surface of methane in the electronic ground state. The generic analytical representation allows for a compact, robust, and flexible description of potentials fur XYn systems irrespective of the specific nature of the atomic interactions. The functions are global in that structures near several minima of the potential hypersurface as well as saddle points and dissociation limits are well described. Clusters of atoms Y-n can be represented as well by this type of function. Care is taken to implement conditions resulting from the symmetric group S-n and to construct positive definite bilinear forms of special functional forms of certain coordinates (such as bond lengths and bond angles), in order to avoid artifacts in exceptional ranges of the potential hypersurface. These special functional forms include intrinsic, symmetry allowed couplings between coordinates such as bending and stretching. We include linear potential terms in bond angle coordinates, which result in effectively quadratic potential terms for highly symmetric structures. True logical multidimensional 01-switching functions S-sw(r) of bond lengths r are used to interpolate between limiting ranges in the hypersurface. The particular form S-sw(r) similar to exp(-(r(sw)/r)(nsw)) allows us to describe the potential as a multipole expansion representation in the lirlit of large r(ix). In the application to methane, first the representations are fitted to data from high level ab initio calculations using multireference configuration interaction techniques. Additional conditions which help to improve the description of experimental data are considered during the fit. Typically, these conditions involve some parameters or parameter groups and refer to the equilibrium geometry and harmonic force field. Other constraints apply to the energies of dissociation channels. We describe the model potentials METPOT 1 to METPOT 4 in the present work.