Animated characters obtained with the skinning method are widely used in movies and video games industry due to its intuitive control and its fast implementation. However, when this method is used for large deformations, the realistic beavior of the animation might be spoiled by the loss of a certain amount of volume of the animated object. Therefore, a method that constraints the volume of a character deformed with an underlying skeleton is set-up. The correction is performed in two steps. First, the surface is deformed with a classical skinning algorithm. Next, the surface is corrected in order to keep its volume constant. The correction is given by a constrained minimisation where the parameters only depend on the skinning data. The method of Lagrange multipliers is used is order to solve the equations. An analytical solution is given that enables the execution at interactive speed. An exact correction of the volume can be applied on the character when the axes are treated separatedly. A correction that locally depend on the shape of the object is also carried on via an approximated correction. The error of the approximated volume is less than 5% in the worst case. This method enables a deformation with a constant volume while keeping the advantage of the skinning. Moreover, the correction is linked to the parameters that are already given for a deformation performed with an animation-skeleton. Therefore, there is no need of any extra work for the artist. Finally, different visual effects can be obtained depending on the type of function that is optimized.