Nowadays there are many technologies and design tools available to accurately obtain and model the geometric shape and the color of objects. However, these methods are not able to provide any information about the elasticity of the objects. This thesis presents a general-purpose scheme for measuring, constructing and representing geometric and elastic behavior of deformable objects without a priori knowledge on the shape and the material that the objects under study are made of. The proposed solution is based on an advantageous combination of neural network architectures and an original force-deformation measurement procedure. An innovative non-uniform selective data acquisition algorithm based on self-organizing neural architectures (namely neural gas and growing neural gas) is developed to selectively and iteratively identify regions of interest and guide the acquisition of data only on those points that are relevant for both the geometric model and the mapping of the elastic behavior, starting from a sparse point-cloud of an object. Multi-resolution object models are obtained using the initial sparse model or the (growing or) neural gas map if a more compressed model is desired, and augmenting it with the higher resolution measurements selectively collected over the regions of interest. A feedforward neural network is then employed to capture the complex relationship between an applied force, its magnitude, its angle of application and its point of interaction, the object pose and the deformation stage of the object on one side, and the object surface deformation for each region with similar geometric and elastic behavior on the other side. The proposed framework works directly from raw range data and obtains compact point-based models. It can deal with different types of materials, distinguishes between the different stages of deformation of an object and models homogeneous and non-homogeneous objects as well. It also offers the desired degree of control to the user.