The transfer of geometrical data from CAD (Computer Aided Design) to FEA (Finite-Element Analysis) is a bottleneck of automated design optimization procedures, yielding a loss of accuracy and cumbersome software couplings. Isogeometric analysis methods propose a new paradigm that allows to overcome these difficulties by using a unique geometrical representation that yields a direct relationship between geometry and analysis. In this study, we investigate its use for sensitivity analysis and more specifically shape gradient computations, in the framework of linear elasticity problems. The potential of isogeometric analysis methods for shape gradient computations is demonstrated for two- and three-dimensional design problems.