By employing the Lanczos method, the effective valence bond model (EVB) is exactly solved for a series of conjugated hydrocarbons with four-membered rings. Several indices calculated from the EVB ground-state energies and wave functions are applied to interrelate with bond lengths, stabilities, and reactivities of these systems. Our results agree well with related experimental observations and deductions of molecular orbital theory. The failure of the classical valence bond theory in these systems is also exposed.