For large-scale problems, especially those related to finite element analysis of viscoelastic flows, the development of less-memory-directed method is still a great issue. In this paper, we present a new data storage method, which we refer to as a 'box' storage (BOX) algorithm, since the coefficient matrix is set up with 'blocks', and each block with 'boxes'. The 'box' is an elementary unit, and all non-zero data are stored only in the 'boxes' in a compact and regular form. We introduced this algorithm for a constitutive equation using a conjugate gradient squared (CGS) method as a solver, so as to maximize the merit of the BOX algorithm. For momentum and continuity equations, we adopted the pressure projection (PP) method, as a segregated scheme, which enables us to solve each velocity component equation separately, in much smaller size, with a continuity constraint. We performed the numerical analysis of die-swell flow of viscoelastic fluids with BOX-PP algorithm, that is, a combination of the BOX and PP algorithms. The new, scheme enabled us to predict the simulation at Weissenberg number (We) = 150, with smaller storage and CPU time requirements, and the results agreed excellently with those obtained by a decoupled finite element analysis.