Silicon nitride (Si3N4) 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 Si3N4 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 Si3N4 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 Si3N4 Brillouin gain at 25 GHz is estimated as 4×10−13 m/W. Moreover, the magnitude of the Si3N4 photoelastic constant is estimated as |p12|=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 Si3N4 to handle high optical power, central for integrated nonlinear photonics.