We present the results of a study of the elastic properties of Gd5Si2Ge2, an alloy with giant magnetocaloric, magnetostrictive, and colossal magnetoresistive properties. Sound wave velocities measured in a number of different geometries allowed us to determine the whole elastic tensor for the monoclinic phase of this material. The anisotropy of the crystal is explored using the polar plots of the variations in the main crystallographic planes of the sound speed, the Young’s modulus, the shear modulus, and the linear compressibility. The effect of hydrostatic pressure on the Gd5Si2Ge2 properties is clarified. The acoustical axes are determined. The bulk modulus is estimated as 68.5 GPa; the Debye temperature is 250 K.