Silicon nitride (Si_{3}N_{4}) has emerged as a promising material for integrated nonlinear photonics and has been used for broadband soliton microcombs and low-pulse-energy supercontinuum generation. Therefore, understanding all nonlinear optical properties of Si_{3}N_{4} is important. So far, only stimulated Brillouin scattering (SBS) has not yet been reported. Here we observe, for the first time, backward SBS in fully cladded Si_{3}N_{4} waveguides. The Brillouin gain spectrum exhibits an unusual multipeak structure resulting from hybridization with high-overtone bulk acoustic resonances of the silica cladding. The reported intrinsic Si_{3}N_{4} Brillouin gain at 25 GHz is estimated as 4×10^{-13} m/W. Moreover, the magnitude of the Si_{3}N_{4} photoelastic constant is estimated as |p_{12}|=0.047±0.004, which is nearly 6 times smaller than for silica. Since SBS imposes an optical power limitation for waveguides, our results explain the capability of Si_{3}N_{4} to handle high optical power, central for integrated nonlinear photonics.