This paper investigates the motion of two infinitesimal masses on the location and stability of the equilibrium points in Robe’s restricted problem of 2 + 2 bodies with the bigger primary a Roche ellipsoid and the smaller a triaxial body. We suppose the bigger primary of mass m1 to be filled with a homogeneous incompressible fluid of density ρ1. The third and the fourth bodies (of mass m3 and m4 respectively) are small solid spheres of density ρ3 and ρ4 respectively inside the ellipsoid, with the assumption that the mass and the radius of the third and the fourth body are infinitesimal. We assume that m2 is describing a circle around m1. The masses m3 and m4 mutually attract each other, do not influence the motion of m1 and m2 but are influenced by them. We have taken into consideration all the three components of the pressure field in deriving the expression for the buoyancy force viz (i) due to the own gravitational field of the fluid (ii) that originating in the attraction of m2 (iii) that arising from the centrifugal force. In this paper, equilibrium solutions of m3 and m4 and their linear stability are analyzed.