Monte Carlo simulations on a cubic lattice were carried out to study the micellization and solubilization of a system containing ABA triblock copolymers, small molecules compatible with the A block, and solvent which selectively solvates the B blocks. The parameters varied were the amount of small molecules, the polymer concentration, the interaction parameters between A and B, A and solvent, solute and solvent, solute and B block, and the A and B block sizes. The corresponding effects on the fraction of polymers forming micelles, the aggregation number of insoluble blocks, the fraction of solutes solubilized, the micelle-solvent partition coefficient of the solubilizates, and the solubilization capacity of the insoluble block were discussed and compared with experimental and theoretical data from the literature.