Nacre causes the shining beauty of pearl due to its remarkable layered structure, which is also strong. We reconsider a simplified layered model of nacre proposed previously [Okumura and de Gennes, Eur. Phys. J. E 4, 121 (2001)] and obtain an analytical solution to a fundamental crack problem. The result asserts that the fracture toughness is enhanced due to a large displacement around the crack tip (even if the crack-tip stress is not reduced). The derivation offers ideas for solving a number of boundary problems for partial differential equations important in many fields.