A comparative study was conducted to determine the range in which the stability of earth and rockfill dams’ upstream and downstream slopes is unaffected by the thickness of a vertical core or an upstream inclined core. Earth and rockfill dam of height 180 m on strong foundation with no berms was chosen for stability analysis in the present study. Different sections of dam with varying core thicknesses for vertical core and varying upstream inclinations and thicknesses of upstream inclined cores were analyzed for identifying the critical thickness under end of construction and steady state seepage conditions beyond which downstream slope of dam exhibited reduction in factor of safety. The influence of two parameters on critical core thickness was analyzed such as relative strength parameters of core to shell and pore pressure ratio ru. This study shows that under end of construction condition for both upstream inclined core and vertical core the critical thickness is approximately 220 m, i.e., 120% of height of dam. Whereas in case of steady-state-seepage condition, upstream inclined critical thickness is 275 m, i.e., 150% of height of dam and core does not influence the stability of outer slopes while for vertical core the critical thickness is 220, i.e., 120% height of dam. Thus, for the same height of dam upstream inclined core is more stable for wider thickness of core as compared to vertical core under end-of-construction and steady-state-seepage condition.