Previously measured in situ x-ray diffraction is used to assess the development of internal elastic strains within grains of a sample of polycrystalline cobalt plastically deformed up to a pressure of 42.6 GPa. An elastoplastic self-consistent polycrystal model is used to simulate the macroscopic flow curves and internal strain development within the sample. Input parameters are single-crystal elastic moduli and their pressure dependence, critical resolved shear stresses, and hardening behavior of the slip and twinning mechanisms which are active in Co crystals. At 42 GPa, the differential stress in hcp-Co is 1.9±0.1 GPa. The comparison between experimental and predicted data leads us to conclude that: (a) plastic relaxation plays a primary role in controlling the evolution and ordering of the lattice strains; (b) the plastic behavior of hcp-Co deforming under high pressure is controlled by basal and prismatic slip of ⟨a⟩ dislocations, and either pyramidal slip of ⟨c+a⟩ dislocations, or compressive twinning, or both. Basal slip is by far the easiest and most active deformation mechanism. Elastoplastic self-consistent models are shown to overcome the limitations of models based on continuum elasticity theory for the interpretation of x-ray diffraction data measured on stressed samples. They should be used for the interpretation of these experiments.