A near-equilibrium potential energy surface has been calculated for cyano-acetylene, HC3N, by means of the coupled electron pair approximation (CEPA) using a basis set of 118 contracted Gaussian-type orbitals, and from it vibration-rotation coupling constants alpha(v) and 1-type doubling constants q(t) and q(t)J have been calculated for various isotopomers by standard perturbation theory. By the combination of experimental B0 and theoretical alpha(v) values for six different isotopomers we were able to determine an accurate equilibrium geometry: r(e)(HC(1)) = 1.0624 angstrom, R1e(C(1)C(2)) = 1.2058 angstrom, R2e(C(2)C(3)) = 1.3764 angstrom and R3e(C(3)N) = 1.1605 angstrom. A conservative estimate of the error in the equilibrium bond lengths is 0.0005 angstrom.