A two fluid hydrodynamical model describing the modification of a stellar wind flow due to its interaction with galactic cosmic-rays is investigated. The two fluids consist of the thermal stellar wind gas and the galactic cosmic-rays. A polytropic one fluid model is used to describe the stellar wind gas, and the cosmic-rays modify the wind via their pressure gradient. The cosmic-rays are considered to be a hot low density gas of negligible mass flux, but with a significant pressure and energy flux compared to the thermal gas. The equations used are essentially those employed in two fluid hydrodynamical models of cosmic-ray shock acceleration by the first order Fermi mechanism, but suitably modified to apply in a spherical geometry and including the effects of gravity on the flow. The stellar wind consists of a transonic flow with a termination shock, and subsonic flow outside the shock. The model shows the deceleration of the wind upstream of the shock by the positive galactic cosmic-ray pressure gradient. The dissertation first discusses the fluid polytropic stellar winds and how to insert shocks in the flow. The hydrodynamical equations governing cosmic-ray modified winds are then introduced followed by a discussion of the physics of the interaction between the thermal stellar wind and the cosmic-rays. A description of the singularities of the equations is also presented. The system of equations is first solved by a finite difference method in the test particle approximation in which the cosmic-rays do not modify the flow, with appropriate boundary conditions applied at infinity, at the wind termination shock, and at the star. A perturbation scheme to determine the modification of the wind by the cosmic-rays is then developed. This scheme applies when the modification of the wind by the cosmic-rays is sufficiently small. Finally a numerical iteration is employed to exactly solve the equations. This latter method has the advantage that it can be applied when there is a considerable modification of the wind by the cosmic-rays.