T2SOLV is an enhanced package of matrix solvers for the TOUGH2 family of codes. T2SOLV includes all the Preconditioned Conjugate Gradient (PCG) solvers used in T2CG1, the current solver package, as well as LUBAND, a new direct solver and DLUSTB, a PCG solver based which implements the BiCGSTAB(m) method. LUBAND, the new direct solver, is faster, more reliable and capable of solving problems orders of magnitude larger than the MA28 routine which it replaces. A significant capability of T2VOC is two types of matrix preprocessing, which make possible the solution of a class of challenging numerical problems (previously tractable only with direct solvers) using the PCG routines. For regular grids, the size of problems tractable with direct solvers is doubled by implementing a D4 alternative diagonal gridblock ordering option.