The structure of collective bands in ^74,76Kr is studied within the framework of the deformed configuration mixing shell model based on Hartree-Fock states. The active single-particle orbits are 1p_3/2, 0f_5/2, 1p_1/2 and 0g_9/2 with ⁵⁶Ni as the inert core. A modified Kuo interaction has been used for the above configuration space. The ⁷⁴Kr nucleus is found to be the most deformed nucleus among the krypton isotopes which is in agreement with experiment. The deformation is found to decrease for the ⁷⁶Kr isotope. The calculated positive- and negative-parity bands agree quite well with the experiment for both the nuclei. A number of excited bands is also predicted. We have also calculated B(E2) values and compared them with available experimental data. The structure of the strongly coupled band built on K = 4^{( + )} in ⁷⁶Kr is also studied.