An ophthalmic laser system is disclosed for removing cataractous tissue from the lens capsule of an eye by phacofragmentation of the lens tissue for subsequent aspiration of the treated tissue. More specifically, a cutting laser is provided which creates a plurality of computer controlled and directed incisions in various strata through the lens tissue. Within each stratum, each incision is computer controlled and is made in the direction from a posterior to an anterior position. The strata are stacked on each other in the posterior-anterior direction, and each includes a plurality of minute incisions. The most posterior stratum of incisions is created first by referencing the cutting laser back into the lens tissue from the posterior capsule. Subsequent, more anterior strata, are created by referencing the cutting layer from the tissue treated by the previous stratum of incisions. In each stratum, the vapors which result from the incisions infiltrate between the layers of the lens tissue fragmenting and liquefying the tissue. The computer controlled device can automatically determine locations and dimensions of incisions, as well as automatically adjusting incision curvature and beam intensity as the incision point is moved from stratum to stratum. After the device liquifies the lens tissue it can then be aspirated.