A biporous medium is a porous medium that shows two independent connected pore systems as; e. g., heat exchanger metal foams or organs. Wave propagation in such media is investigated by upscaling the pore scale description. We focus on the multiphasic macroscopic behaviour which corresponds to Biot's model for one pore system porous media. In the case of isotropy, one shear wave and three dilatational waves are pointed out. The domain of validity of the model is for the pore scale dimensionless number - the ratio of the pressure term to the viscous term in the Stokes equation - Ql =|partial derivative p(F)/\/partial derivative X-j |/|mu partial derivative(2)v(i)(F)/partial derivative X-j partial derivative X-j |= O(epsilon(-1)), where epsilon is the parameter of separation of scales. When Q(l) = O(1) or Q(l) = O(epsilon), the macroscopic model is monophasic elastic or monophasic viscoelastic, respectively, just as for porous media with a single pore system. To easily choose the right model to be used to describe a given biporous medium in between the three macroscopic models, number Q(l) is evaluated as a function of the biporous material properties, only. We show that wave propagation in both heat exchanger metal foams and organs follows a multiphasic macroscopic behaviour.