A detailed theoretical study of structural and magnetic behaviors of cubic cobalt and nickel along the bcc-fcc (Bain) transformation paths as well as of hcp cobalt and nickel loaded uniaxially along the (0001) direction at various atomic volumes is presented. Stability of possible ferromagnetic phases of bcc nickel is analyzed. The calculated contour plots of total energy are used to explain and predict the lattice parameters and magnetic states of tetragonal and hcp cobalt and nickel overlayers on various (001) or (111) substrates, respectively. In case of tetragonally deformed structures, the stresses needed to keep the thin films coherent with the substrates are also determined and all Co and Ni overlayers on (001) cubic substrates are predicted to be ferromagnetic. It is shown that the lattice parameters of Co and Ni overlayers may be very well understood in terms of properties of appropriately deformed bulk Co and Ni.