A Volume of Fluid (VOF) method is applied to investigate the deformation and breakup of an initially spherical drop in the bag- and shear breakup regimes, induced by steady disturbances. The onset of breakup is sought by studying steady-shape deformations while increasing the Weber number until breakup occurs. A parameter study is carried out applying different material properties and a wide range of drop Reynolds numbers in the steady wake regime. Density ratios of liquid to gas of 20, 40, and 80, viscosity ratios in the range 0.5-50, and Reynolds numbers between 20 and 200 are investigated for a constant Weber number of 20. The critical Weber number is found to be 12, in agreement with observations of earlier studies. For Weber number of 20 varying density, viscosity ratios and Reynolds numbers, interesting mixed breakup modes are discovered. Moreover, a new regime map including all modes observed is presented. A criterion for the transition between bag-and shear breakup is defined relating the competing inertial and shear forces appearing in the flow. Furthermore, results on breakup times and the time history of the drag coefficient are presented; the latter is concluded to be a potential parameter to indicate the occurrence of breakup. (C) 2014 Elsevier Ltd. All rights reserved.