Nowadays, it is commonly admitted that the aesthetic appearance of a product has an enhanced role in its commercial success. Therefore, understanding and manipulating the aesthetic properties of shapes in the early design phases has become a very important field of research. There exists an appropriate vocabulary for describing the aesthetic properties of 2D free-form curves that includes terms such as straightness, acceleration, convexity and tension, which are normally used by stylists when describing and modifying shapes. However, the relationships between this vocabulary and the geometric models are not well established. This work investigates the possibility of applying Machine Learning Techniques (MLT) to discover possible classification patterns of 2D free-form curves with respect to the so-called straightness of the curve. First, we verified that MLT can correctly (99.78%) reapply the classification to new curves. In addition, we verified the abilities of the Attribute Selection methods to identify the most important attributes for the considered classification, among a larger set of attributes. As a result, it was possible to recognize as the most characterizing parameters the same curve attributes previously used to compute the measure of straightness (S). Moreover, Linear Regression (LR) was able to extract automatically an exact mathematical model, which can correlate the geometric quantities with the class of the curve, congruent to one we previously specified. This work indeed demonstrates that MLT are very suitable and can be efficiently used in this context. The work is a first step towards the characterization and classification of free form surfaces giving the general directions on how MLT can be exploited to characterize free-form surfaces with respects to the aesthetic properties.