When urban distribution systems are gradually modernized, the overhead lines are replaced by underground cables, whose shunt admittances can not be ignored. Traditional power flow (PF) model with π equivalent circuit shows non-convexity and long computing time, and most recently proposed linear PF models assume zero shunt elements. All of them are not suitable for fast calculation and optimization problems of modern distribution systems with non-negligible line shunts. Therefore, this paper proposes a linearized branch flow model considering line shunt (LBFS). The strength of LBFS lies in maintaining the linear structure and the convex nature after appropriately modeling the π equivalent circuit for network equipment like transformers. Simulation results show that the calculation accuracy in nodal voltage and branch current magnitudes is improved by considering shunt admittances. We show the application scope of LBFS by controlling the network voltages through a two-stage stochastic Volt/VAr control (VVC) problem with the uncertain active power output from renewable energy sources (RESs). Since LBFS results in a linear VVC program, the global solution is guaranteed. Case study exhibits that VVC framework can optimally dispatch the discrete control devices, viz. substation transformers and shunt capacitors, and also optimize the decision rules for real-time reactive power control of RES. Moreover, the computing efficiency is significantly improved compared with that of traditional VVC methods.