Roadway deformation and rock burst are the two key challenges faced by the safe operation of coal mines. Aiming at the issue of large deformation of the gob-side roadway under coal pillars in multiseam mining, this study has considered the case of the 8308 panel of Xinzhouyao coal mine in China. Based upon a combination of theoretical analysis, numerical simulations, and engineering practices, the mechanical model of “stress and deformation quantitative calculation of gob-side roadway under overlying coal pillars” was established in this study. The analytical solutions of the vertical stress distribution and the plastic zone of the gob-side roadway under overlying coal pillars were obtained. Finally, the accuracy of the mechanical model was verified using numerical simulations. The results showed that the coal pillar, upright above the gob-side roadway, and the cantilever roof around the gob-side roadway were the main factors leading to stress concentration and deformation around the gob-side roadway. For the particular cases considered in this study, the peak stress of the gob-side roadway could reach 1.8 times of the self-weight stress of overlying strata. The rates of the contribution of the gob-side roadway’s overlying pillar and the cantilever roof around the gob-side roadway to peak stress were 78.3% and 16%, respectively. The obtained results have an essential reference significance for stress calculations and rock burst prevention design of gob-side roadway under overlying coal pillars in multiseam mining.