The Morrey Conjecture pertains to the properties of quasi-convexity and rank-one convexity in functions, where the former implies the latter, but the converse relationship is not yet established. While Sverak has proven the conjecture in three dimensions, it remains unresolved in the two-dimensional case. Analyzing these properties analytically is a formidable task, particularly for vector-valued functions. Consequently, to investigate the validity of the Morrey Conjecture, we conducted numerical simulations using a set of example functions by Dacorogna and Marcellini. Based on our results, the Morrey Conjecture appears to hold true for these functions.