The interpretation of plastic deformation experiments on quasicrystals is a challenging task due to the occurrence of changes of the structure during deformation. In this paper, we present a quantitative model for quasicrystal plasticity on the basis of a constitutive-equations Ansatz, which takes these effects into account. A single-internal-variable model of the kind commonly used for describing crystal plasticity, is adapted for the description of the dislocation density evolution in a quasicrystal. In addition, we introduce a structural parameter that accounts for the evolution of order in the course of plastic deformation. The numerical solution of the resulting set of evolution equations yields the flow stress and the dislocation density as a function of strain, which can be directly compared to corresponding experimental curves obtained on icosahedral Al-Pd-Mn. An excellent agreement between experiment and the calculated curves obtained using our model is found.