Oxygen transport from a systemic capillary to its surrounding tissue region in the hyperbaric environment is analyzed. Longitudinal and transversal diffusion in the capillary and tissue regions, convective effect of the blood, and equilibrium chemical kinetics of oxygen with hemoglobin are studied in this model. The effect of capillary wall permeability and capillary wall pressure gradient constant on the oxygen transport is also investigated in this study. The nonlinear oxyhemoglobin dissociation curve is considered at hyperbaric environment; further, the zeroth- and first-order oxygen uptake kinetics are considered for the oxygen consumption by the tissue cells. The analytical solution for the oxygen transport in both capillary and tissue regions is obtained using the method of eigenfunction expansion. It is noticed that the amount of oxygen consumption in the tissue region is larger with the first-order metabolism than the zeroth-order metabolism. It is also seen that in the first two-fifth part of the tissue, oxygen is delivered by longitudinal and transversal diffusion, and in the rest of the tissue, it is transported by transversal diffusion only.