The superconductivity of the multi-phased sample of (La//0//. //9Sr//0//. //1)//2CuO//4// minus //y has been studied under hydrostatic pressure to 2. 0 GPa and quasihydrostatic pressure to 4. 2 GPa. The superconducting transition temperature (T//c) increases initially with increasing pressure. The results of the critical current and the diamagnetic susceptibility measurements, and the high sensitivity of T//c to the hydrostaticity of pressure suggest that the superconductivity of the high T//c phase in this multi-phased material is of bulk and highly anisotropic in nature, while that of the low T//c phase is of interfacial nature.