The effect of pressure on the structure and mobility of Sperm Wale Apomyoglobin was studied by Molecular Dynamics computer simulation at 1 bar and 3 kbar (1 atm=1.01325 bar=101.325 kPa). The results are in good agreement with the available experimental data, allowing further analysis of other features of the effect of pressure on the protein solution. From the analysis of Secondary Structures (SS) along the trajectories it is observed that alpha-helixes are favoured under pressure at the expense of bends, turns and 3-helixes. The studies of mobility show that although the general mobility is restricted under pressure this is not true for some particular residues. The studies of tertiary structure show important conformational changes. The evolution of the Solvent Accessed Surface (SAS) with pressure shows a notorious increase due almost completely to a biased raise in the hydrophobic area exposed, which consequently shows that the hydrophobic interaction is considerably weaker under high hydrostatic pressure conditions.