The maximum stress intensity factors, K_I,kmax(θ) and K_II,kmax(θ), of three non-parallel oblique cracks were calculated to reveal the interaction mechanism of multiple cracks. The multiple crack initiation criterion was adopted to predict the non-parallel multiple crack initiation parameters. Uniaxial compression tests were performed on rock specimens (red sandstone) with three non-parallel oblique cracks, where the strain near the crack tips was monitored by the strain gauge measurement method to determine the crack initiation sequence. The results showed that the change of crack relative inclination angle had little effect on the fracture trajectory. Multiple crack tips were seldom initiated at the same time. The failure modes of red sandstone specimens with three non-parallel oblique cracks under uniaxial compression are divided into two types: wing crack penetration and wing crack-secondary crack penetration. All of the fracture mechanisms are Mode I (tensile) initiation. The predicted results coincided well with the test results, verifying the validity of the theoretical results.