WALL Street stocks trod water yesterday, livened only by a run-up in IBM shares that sent the Dow Jones industrials higher by 33.96 points to close at 5,671.68 after a burst of late buying.

Advancing issues had a weak lead on decliners on the New York Stock Exchange. Volume on the Big Board was moderately heavy at more than 300 million shares, and up from Monday's pace. Broad-market indexes were mostly higher

IBM rose as high as 118 1/8, up 7 3/4, after Lehman Brothers, citing an independent research firm, said demand for IBM's core mainframe products was very strong in March.

Advancing issues outnumbered decliners by about eight to seven on the New York Stock Exchange, with 1,260 up, 1,097 down and 775 unchanged. The NYSE's composite index rose 0.66 to 351.60. The Standard and Poor's 500-stock index rose 1.54 to 655.27.