For heavy atoms or ions, such as, Rb and Cs et al., relativistic effect must be considered in the calculation. In this paper, the relativistic many-body perturbation theory is used to solve the Dirac equation. And the zeroth-order hyperfine constants are evaluated with Dirac-Fock wave function. The finite basis sets of dirac equation are constructed by B-splines. With the finite basis sets the core polarization and the correlation diagrams are calculated. The hyperfine structure constants of the 5S1/2 and 6S1/2 states of 85Rb as well as the 6S1/2 and 7S1/2 states of 133Cs are evaluated.