We examined a simple model system of homopolymer solutions in 3D confined between two parallel and nonabsorbing surfaces and in equilibrium with a bulk solution and accurately calculated the effective interaction between the two surfaces using both lattice Monte Carlo (MC) simulations and self-consistent field (SCF) calculations. Our results here, when compared with those in 2D (Zhang, P.; Wang, Q., Macromolecules2019,52, 5777), quantitatively revealed that the fluctuation-induced intermediate-range repulsion between the two surfaces (i.e., the anti-Casimir effect) is about 1 order of magnitude stronger than the repulsion due solely to the finite chain length given by the SCF theory, is weaker but occurs over a broader range of surface separation in 3D than in 2D, and decreases with decreasing solvent quality. We also found for the first time a long-range attraction between the two surfaces (i.e., the Casimir effect) near the critical point of the bulk solution in both MC simulations and SCF calculations.