The ground state potential energy surface of the GeC2 molecule has been investigated at highly correlated coupled cluster levels of theory. Large basis sets including diffuse functions and functions to describe core correlation effects were employed in order to predict the true equilibrium geometry for GeC2. Like the much-studied valence isoelectronic SiC2, the linear ((1)Sigma(+)), L-shaped ((1)A(')), and T-shaped structures ((1)A(1)) must be investigated. The L-shaped C-s geometry is found to have real harmonic vibrational frequencies along every internal coordinate, and the linear stationary point has an imaginary vibrational frequency along the bending mode at every level of theory employed. The T-shaped geometry is found to have an imaginary vibrational frequency along the asymmetric stretching mode. At the coupled cluster with single and double excitations and perturbative triple excitations [CCSD(T)]/correlation consistent polarized valence quadrupole-zeta (cc-pVQZ) level, the nonrelativistic classical relative energies of the T-shaped and linear structures with respect to the L-shaped minimum are 0.1 and 2.8 kcal/mol, respectively. Including zero-point vibrational energy, scalar relativistic, and core-valence corrections, the T-L energy separation is shifted to 0.4 kcal/mol and the relative energy between the L-shaped and linear structures is still 2.8 kcal/mol. All nonrelativistic and relativistic computations predict that the L-shaped ((1)A(')) structure is most favored for the ground state. The linear structure is predicted to be a transition state, as the case of SiC2.