We report the results of {ital ab} {ital initio} local-density-functional total-energy calculations of W(001) slabs of varying thickness as a function of the in-plane or surface lattice parameter. The results are used to isolate the surface strain energy of the ideal surface. We find that the ideal W(001) surface is softer than the bulk and has a small tensile strain of about 1% with a strain energy of less than 1 mRy/(surface atom). A comparison of the strain energy with the energy associated with the reconstruction leads to the conclusions that the interaction between the ideal surface atoms is {ital weak} {ital attractive} and the instability of the ideal W(001) surface is {ital not} the result of a large surface strain.