Geophysical imaging techniques together with numerical models have shown that the surface uplift measured above the Altiplano-Puna Magma Body (APMB) can be resolved by the presence and propagation of a diapir from the top of the APMB itself. In this work we interpret deformations that characterize the crustal region above and around APMB through the employment of a viscoplastic type rheology. That is, we assume that at large scale the ductile lower-middle crust that surround the magmatic mush behaves as yield-stress fluid described by a Herschel-Bulkley (HB) model. In this scenario, the main critical conditions needed for the growth and the subsequent rise of the diapir are: (1) the ratio between yield stress and viscous stresses, namely the Bingham number Bi, has to be less than 1, i.e. Bi ≤1; and (2) the ratio between buoyancy stresses and yield stress, namely the inverse of the Yield number Y_{inv} =Y^{−1} , has to be larger than a critical value, i.e. Y_{inv} > Y_{inv_C}. By using these critical conditions we infer the bulk rheological properties of the heterogeneous lower-middle crust above APMB. We estimate the yield stress of the crust in between 0.5-15 MPa. For a crust that allows the development and the emerge of a 10 to 100 km wide diapir, the coupling of this range of yield stress with the regional uplift velocity measured at the surface allows to estimate a critical strain rate of ∼10^{−15} - 10^{ −16} 1/s and a maximum bulk effective viscosity of the lower-middle crust of ηc=10^{21} Pa.s.