This study explore the tribological performance of bump foil journal bearings (FJBs) equipped with micro-pockets. The influence of micro-pockets on the load capacity (LC) and friction factor (FF) of FJBs is evaluated for various foil materials, including Inconel X750 (IN), Spring steel EN42J (SP), SS 316, Beryllium copper (BC), and Phosphor bronze (PB). The compressible Reynolds equation is solved numerically to assess the tribological behavior of bump FJBs under various operating conditions. Initially, the impact of micro pocket on the tribological characteristics such as load capacity and friction factor of bump FJBs is examined by comparing their performance with plain FJB. Subsequently, the effect of operating parameters such as pocket depth (PD), bearing number (Λ), and eccentricity (ɛ), on the tribological behavior is analysed by using response surface methodology (RSM). The multi-objective grey relational analysis (GRA) technique is employed to determine the optimal values of input variables for each foil material. The findings reveal that micro-pockets enhance the dimensionless LC of bump FJBs beyond a bearing number of 2.061. Moreover, micro-pockets reduce the friction factor of bump FJBs. SS 316 exhibits the most significant impact among the tested foil materials, while phosphor bronze exhibits the least. For SS 316, the optimal values pocket depth (PD), bearing number (Λ), and eccentricity ratio (ɛ) are 3μm, 2.061, and 0.5 respectively. Under these optimal conditions, the LC and FF of bump FJBs are 0.7740 and 13.645, respectively. Micro-pocket reduce the friction factor by 2 to 15%. The pocket depth in bump FJB is significant for the phosphor bronze foil material. Additionally, increasing the pocket depth enhances the dimensionless LC of bump FJBs while decreasing the friction factor.