Computer simulations of perfectly branched dendrimers up to the sixth generation have been performed under the influence of uniaxial elongational flow for the first time for a model with explicit dendritic topology. The Brownian dynamics simulation technique has been applied to a freely jointed bead-rod model with excluded volume both with and without hydrodynamic interactions. The dependence of conformational properties and the intrinsic elongational viscosity on the flow rate were obtained. The coil-stretch transition was observed for dendrimers of all generations with it being less pronounced than the same type of transition observed for a linear polymer chain. Hydrodynamic interactions shift the onset of this transition to higher elongational rates. The transition is observed to occur in two stages as it was for a linear polymer. The dendrimer first orients at low flow rate as a whole along the flow axis without significant deformation and local orientation. Increasing flow rate leads to local orientation on the level of the monomer leading to significant global deformation of the dendrimer. The monomers belonging to inner generations are oriented stronger relative to outer monomers at all flow rates. The intrinsic elongational viscosity of the dendrimer increases with flow and plateaus at high rates. The limiting value of intrinsic elongational viscosity for a model with hydrodynamic interactions at high flow rates is less than its value for a model without these interactions. The onset of the coil-stretch transition occurs at lower elongational rates as the number of monomers, N, within the dendrimer increases. The dependence of the onset of this transition with N is less pronounced than for a linear chain. It becomes less steep with N and is not described by a power law.