Response surface methodology (RSM) is used for mathematical modeling of friction stir welding parameters for joining AA6061 composite material. Characteristics of joints were examined through response characteristics such as ultimate tensile strength (UTS) and microhardness (HV) using RSM. Microstructure examination was carried out using optical microscopy, scanning electron microscopy and electron backscattered diffraction, and results exhibit variation in the grain size diameter. Specifically, lower nugget exhibits fine grains with maximum hardness compared to middle nugget and upper nugget. Analysis of variance (ANOVA) results indicate good match between actual values and predicted values with R2 of 0.91 and 0.96, respectively, for UTS and HV, and better joint efficiency of 90% is obtained. © 2021, The Indian Institute of Metals - IIM.