The water or soft matter is often filled in the fissures of rock masses. The fracture of a rock-mass fissure under the internal pressure is an important problem in the geotechnical engineering. It is simplified as the plane stress problem of a fissure loaded by I mode with a pair of internal point forces in the finite rock mass. The plastic stress fields in the zone near fissure line are solved using the near fissure line method on the basis of the failure criterion of rock bridge material and differential equilibrium equations. By matching the plastic stress fields with the reasonable elastic stress fields at the elastoplastic boundary

relationship between the internal pressures and cracked region lengths on the fissure line is obtained. The bearing capacity of rock bridges is also given.