The volume contains refereed invited and contributed papers presented at the Second Workshop on Large-Scale Scientific Computations held on June 1-6, 1999 in Sozopol, Bulgaria. The topics covered include robust preconditioning algorithms, adaptive and local refinement methods, conservative discretization schemes, multi-scale methods, stability of algorithms in numerical linear algebra, parallel algorithms and performance analysis. Separate sections are devoted to structured matrix computations, matrices with sparsity structure, high-performance methods for convection diffusion and Navier-Stokes problems, computations in image processing, large-scale computations in air pollution modelling, molecular modelling by high performance computational techniques, high performance computing in geomechanics and flow simulation in porous media, large-scale computations for mechanical engineering problems.