Scholastic hylomorphism conceives prime matter and substantial form as metaphysical parts of every physical substance. During the early modern period, both hylomorphic constituents faced significant criticism as scientists and philosophers sought to replace Aristotelianism with physical explanations for the workings of the universe. This paper focuses specifically on prime matter and delves into the arguments put forth by four 16th-century scholastic philosophers – Toledo, Fonseca, Góis, and Suárez – in their attempts to establish the existence of prime matter. Firstly, I (...) analyse a set of arguments rooted in substantial change, which emphasize the crucial role of a persistent, common substrate in the processes of generation and corruption. Secondly, I explore a set of ex-nihilo arguments and, thirdly, I examine a series of demonstrations based on the interplay between accidental and substantial change. Although these three sets of arguments converge on the necessity of a common substrate for substantial change to occur, they fall short of demonstrating that this substrate is both prime and shared by all natural entities. Fourthly, I turn to a set of arguments centred on the impossibility of infinite regress, designed to complement those related to natural change, and I assess additional arguments that do not primarily focus on substantial change. Lastly, I draw my conclusions on these argumentative strategies to demonstrate the existence of prime matter. (shrink)