The behavior of a single liquid drop suspended in another liquid and subjected to simple shear flow is studied numerically using a diffuse interface free energy lattice Boltzmann method. The system is fully defined by three physical, and two numerical dimensionless numbers: a Reynolds number Re, a capillary number Ca, the viscosity ratio lambda, an interface-related Peclet number Pe, and the ratio of interface thickness and drop size (the Cahn number Ch). The influence of Pe, Ch and mesh resolution on accuracy and stability of the simulations is investigated. Drops of moderate resolution (radius less than 30 lattice units) require smaller interface thickness, while a thicker interface should be used for highly resolved drops. The Peclet number is controlled by the mobility coefficient Gamma. Based on the results, the simulations are stable when Gamma is in the range 1-15. In addition, the numerical tool is verified and validated in a wide range of physical conditions: Re = 0.0625 50, lambda = 1, 2, 3 and a capillary number range over which drops deform and break. Good agreement with literature data is observed. (C) 2013 Elsevier Ltd. All rights reserved.