We reported the first Monte Carlo study of incompressible symmetric binary homopolymer blends. Using fast lattice Monte Carlo simulations (Q. Wang, Soft Matter 5 (2009) 4564-4567) in a semi-grand canonical ensemble with the cooperative motion algorithm generalized in our previous work (P. Zhang, Q Wang, J. Phys. Chem. B 118 (2014) 12059-12067) and the finite-size scaling theory, we studied the critical properties of incompressible symmetric blends on the hexagonal lattice. We also used the replica-exchange scheme to greatly improve our sampling, and the multiple histogram reweighting technique to accurately locate the critical point. Instead of the self- and mutual-avoiding walk chain model and the nearest-neighbor interaction used in conventional lattice simulations, here we adopt the model system with multiple occupancy of lattice sites and the Kronecker delta-function interaction, which is the lattice counterpart of the standard model of incompressible bin00ary homopolymer blends used in continuum polymer field theories. This enables direct comparisons between our simulation results and mean-field (Flory-Huggins) predictions without any parameter-fitting (e.g., to determine the Flory Huggins x-parameter). The effects of system fluctuations/correlations on the critical point and phase diagram of incompressible symmetric blends are therefore quantitatively and unambiguously revealed in this work. (C) 2016 Elsevier Ltd. All rights reserved.