In seeking validation of Dissipative Particle Dynamics (DPD) for the mesoscopic modeling of multiphase fluid-fluid systems in external fields, simulations of a pendant drop and a drop in simple shear flow have been performed. The shape profile of the simulated pendant drop was found to be in perfect agreement with that computed by solving the Laplace equation. At increased values of the gravitational force (g), the drop underwent considerable elongation, developing a "neck" between the solid support and its bulk part. Further increases in g resulted in thinning of the neck, which ruptured as gr exceeded a certain value, leading to the detachment of the drop. This picture of the detachment process is consistent with the experimental observations published in the literature. Also, the simulations reproduced the drop volume experiment quantitatively. For the drop in shear flow, the degree of deformation was found to be a linear function of the capillary number (Ca) in the region Ca less than or equal to 0.11, in good agreement with Taylor's theory; this is despite the fact that the hydrodynamic regime in the simulations (Re similar to 1-10) is quite different from that assumed in the theory (Re much less than 1). At increased shear rates the results showed positive departure from linearity, in agreement with theory and experiment. Further increases in Ca resulted in the drop assuming a dumbbell like shape, the middle part of the "dumbbell" gradually stretching to form a thin neck. The rupture of the neck was occasioned by the instabilities manifested in the form of stochastic oscillations which magnified as the critical point was reached. The time evolution of the shape of the drop as it underwent the breakup process in our simulations bears remarkable similarity to the experimental observations of Torza et al. The critical value of the capillary number obtained in the simulations is in reasonable agreement with the experimental figure.