Ex vivo biomechanical testing of growth plate samples provides essential information about its structural and physiological characteristics. Experimental limitations include the preservation of the samples since working with fresh tissues involves significant time and transportation costs. Little information is available on the storage of growth plate explants. The aim of this study was to determine storage conditions that could preserve growth plate biomechanical properties. Porcine ulnar growth plate explants (n = 5 per condition) were stored at either 4 °C for periods of 1, 2, 3, and 6 days or frozen at −20 °C with slow or rapid sample thawing. Samples were tested using stress relaxation tests under unconfined compression to assess five biomechanical parameters. The maximum compressive stress (σmax) and the equilibrium stress (σeq) were directly extracted from the experimental curves, while the fibril-network reinforced biphasic model was used to obtain the matrix modulus (Em), the fibril modulus (Ef), and the permeability (k). No significant changes were observed in σeq and Em in any of the tested storage conditions. Significant decreases and increases, respectively, were observed in σmax and k in the growth plate samples refrigerated for more than 48 h and in the frozen samples, when compared with the fresh samples. The fibril modulus Ef of all stored samples was significantly reduced compared to the fresh samples. These results indicate that the storage of growth plates in a humid chamber at 4 °C for a maximum of 48 h is the condition that minimizes the effects on the measured biomechanical parameters, with only Ef significantly reduced. Refrigerating growth plate explants for less than 48 h maintains their maximal stress, equilibrium stress, matrix modulus, and permeability. However, cold storage at 4 °C for more than 48 h and freezing storage at −20 °C significantly alter the biomechanical response of growth plate samples. Appropriate growth plate sample storage will be beneficial to save time and reduce transportation costs to pick up fresh samples.