Heavy selling in auto, banking and telecom stocks weighed on the indices, analysts said.
The Sensex settled at 41,253.74, lower by 304.26 points or 0.73 per cent from the previous close of 41,558.
It had opened at the day's high of 41,607.49 and touched an intra-day low of 41,184.73.
The Nifty50 on the National Stock Exchange (NSE) closed at 12,168.45, lower by 87.40 points or 0.71 per cent from its previous close.
"Market witnessed thin trade on the last trading day of the year with investors shying away from taking fresh position on concerns that government will breach its fiscal deficit target," said Vinod Nair, Head of Research, Geojit Financial Services.
"Markets wrapped up 2019 on the higher side. Nifty had given a return of 12 per cent while mid and small-caps underperformed by (-)5 per cent and (-)11 per cent, respectively. The market is currently witnessing a navigation of fund flow from large cap to mid-caps in expectation of government policies and positive global environment which will support investors' sentiment," Nair added.
Among the stocks on the Sensex, NTPC gained the most on Tuesday by 2.01 per cent. The only other gainers on the index were ONGC (0.63 per cent), Sun Pharmaceutical (0.60 per cent) and PowerGrid (0.03 per cent).
The stocks which lost the most on Sensex were Tech Mahindra (lower by 2.51 per cent), Bajaj Auto (2.08 per cent), Reliance Industries (1.95 per cent), Hero MotoCorp (1.41 per cent) and IndusInd Bank (1.31 per cent).
( With inputs from IANS )