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In-plane cleavage directions of two dimensional (2D) crystals are displayed and often well-defined in their flakes exfoliated by the mechanical exfoliation method. Here, we investigate the correlation between dominant in-plane cleavage direction and elastic properties in different directions. CrPS₄ flakes show a preferential in-plane cleavage direction of 67.5°, corresponding to <110> direction. To explain it, we calculated the directional dependence of Young’s modulus and fracture energy using first-principles density functional theory calculations. We found that fracture energy is directly relevant to the in-plane cleavage direction of CrPS₄. Our study can provide a facile approach to figure out the direction of 2D crystals without complex characterization process, which is valuable for material processing of 2D materials.