We investigate how cluster morphology is affected by the cosmological constant in low-density universes. Using high-resolution cosmological N-body/smoothed particle hydrodynamics simulations of. at cold dark matter (LambdaCDM; Omega(0) = 0.3; lambda(0) = 0.7) and open cold dark matter (OCDM; Omega(0) = 0.3, lambda(0) = 0) universes, we calculate statistical indicators to quantify the irregularity of the cluster morphologies. We study axial ratios, center shifts, cluster clumpiness, and multipole-moment power ratios as indicators for the simulated clusters at z = 0 and 0.5. Some of these indicators are calculated for both the X-ray surface brightness and projected mass distributions. In LambdaCDM all these indicators tend to be larger than those in OCDM at z = 0. This result is consistent with the analytical prediction of Richstone, Loeb, & Turner, that is, clusters in LambdaCDM are formed later than in OCDM and have more substructure at z = 0. We perform a Kolmogorov-Smirnov test on each indicator for these two models. We then find that the results for the multipole-moment power ratios and the center shifts for the X-ray surface brightness are under the significance level (5%). Our results also show that these two cosmological models can be distinguished more clearly at z = 0 than at z = 0.5 by these indicators.