Earth and rockfill dams can be constructed having vertical or upstream inclined core with varying thicknesses. The thickness of the core for vertical and upstream inclined core depends upon the quantity of fine grained and coarse-grained materials available at site. This paper presents analytical study carried out for the thick upstream inclined core to determine the critical thickness of inclined core under Steady-State-Seepage condition (SSS). Stability analysis for 180 m high earth and rockfill dam with an upstream slope of 1 in 2.70 and a downstream slope of 1 in 1.90 was carried out. A simplified section of dam with clay core of varying upstream inclination along with variation of base thickness of the core from 60 to 650 m was analyzed. Parametric study with respect to relative strength parameters of core to shell was also carried out with varying thickness of inclined core. This paper presents critical thickness of upstream inclined core with in which factor of safety (FoS) of downstream side slope of the dam would be safe. The critical thickness of core was found to be 275 m and critical slope of core has been arrived for both upstream and downstream slope as 1 V: 086 H and 1 V: 0.55 H, respectively.