A month's worth of rain is set to fall in Melbourne over the next two days, with thunderstorms and hail likely to accompany the downpour.

The Bureau of Meteorology is predicting up to 15 millimetres of rain for Thursday, with another 25 to 80 millimetres expected on Friday - almost up to double the average May rainfall of 56 millimetres.

Senior forecaster Rod Dickson said a powerful cold front arriving on Thursday could produce hail, and will see a good dump of snow of down to 900 metres in the state's alpine areas.

"We are going to see a front come through (on Wednesday night) which will produce five millimetres of rain.