Australian shares have closed out the financial year with a rally following a strong lead from Wall Street overnight, as the see-saw action continues for the fourth day.

The benchmark S&P/ASX200 index closed Tuesday up 82.9 points, or 1.43 per cent, at 5,897.9 points, while the broader All Ordinaries index was up 85.7 points, or 1.45 per cent, at 6,001.3.

Meanwhile, the Australian dollar was buying 68.54 US cents, down from 68.84 US cents at the close of trade on Monday.