The effects of spin-orbit coupling on the atomic and electronic structures of clean W(110) surface and Sn deposited W(110) surface are studied using the Density Functional Theory. While the relaxed atomic geometry remains unaffected, there are changes in the surface electronic states with the inclusion of spin-orbit coupling. For the clean W(110) surface, we have identified a total of three surface and one resonance states, and discussed the anisotropic behaviour of Dirac-like states. With increasing Sn monolayer coverages on the W(110)-(1x4) slab, the Dirac-like cone behaviour is found to progressively distort, and Sn-derived states develop. For a (1x1) prototypical model of monolayer Sn coverage, we have calculated the maximum splittings of 0.10 eV and 0.52 eV for the two surface states characterised mainly by the W 3d(5/2) and W 3d(3/2) orbitals.