Industrial proteins from agriculture of either animal or vegetable origin, including their peptide derivatives, are of great importance, from the qualitative and quantitative point of view, in food formulations (emulsions and foams). A fundamental understanding of the physical, chemical, and functional properties of these proteins is essential if the performance of proteins in foods is to be improved and if underutilized proteins, such as plant proteins (and their hydrolysates and peptides derivatives), are to be increasingly used in traditional and new processed food products (safe, high-quality, health foods with good nutritional value). In this contribution we have determined the main physicochemical characteristics (solubility, composition, and analysis of amino acids) of a sunflower protein isolate (SPI) and its hydrolysates with low (5.62%), medium (23.5%), and high (46.3%) degrees of hydrolysis. The hydrolysates were obtained by enzymatic treatment with Alcalase 2.4 L for DH 5.62 and 23.5% and with Alcalase 2.4 L and Flavorzyme 1000 MG sequentially for DH 46.3%. The protein concentration dependence on surface pressure (surface pressure isotherm), a measure of the surface activity of the products (SPI and its hydrolysates), was obtained by tensiometry. We have observed that the degree of hydrolysis has an effect on solubility, composition, and content of the amino acids of the SPI and its hydrolysates. The superficial activity and the adsorption efficiency were also affected by the degree of hydrolysis.