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The magnetic anisotropy properties of the ferromagnetic semiconductor (Ga,Mn)(As,P) are studied in a material-specific microscopic k.p approach. We calculate the band diagram and the density of states of such quaternary ferromagnetic alloys using a 40 band k.p model as well as antiferro- magnetic s,p-d exchange interaction. Our simulations clearly show that the uniaxial and cubic magnetic anisotropy parameters reveal a pronounced dependence on the vertical strain. We also show that the microscopic calculations are in good agreement with the theoretical and experimental results especially in the description of the fourth-order in-plane and out-of-plane components of the magnetic anisotropy. The anisotropy constants obtained from the microscopic calculations allow us to construct a three-dimensional magnetic free energy surface, which clearly indicates that the easy axis of magnetization depends on the strain conditions.