First principle calculations are performed using the super cell method with pseudopotentials and plane waves based on the Density Functional Theory (DFT) for the surface structural properties at T = 0 K. Thin slabs of 7 - 13 atomic layers of the clean Nb and Ta (001) surfaces are considered and relaxations, surface energies, and work functions of the fully relaxed slabs are presented. Consistent results are obtained with the Generalized Gradient Approximation (GGA) and the Local Density Approximation (LDA) for the exchange-correlation functional and they compare well with experimental and other theoretical works.