On My Own by Peach first appeared on the Israeli foreign-music chart on 24 Sep 1996, entering at #16. It peaked at #5 on 15 Oct 1996. In total it spent 7 weeks on the chart, last charting on 4 Nov 1996.
| Wk | Date | Pos |
|---|---|---|
| 1 | 24 Sep 1996 | 16 |
| 2 | 1 Oct 1996 | 13 |
| 3 | 8 Oct 1996 | 7 |
| 4 | 15 Oct 1996 | 5 |
| 5 | 22 Oct 1996 | 15 |
| 6 | 29 Oct 1996 | 22 |
| 7 | 4 Nov 1996 | 30 |