Three males have been charged following a police investigation into a series of alleged robberies and other offences across Melbourne's south-eastern suburbs.

Victoria Police said two 16-year-old boys and an 18-year-old man were arrested after detectives investigated a group allegedly involved in multiple offences during September. Police are investigating 21 incidents, including alleged bag snatches, home invasions, car thefts and petrol drive-offs.

Investigators allege two cars were stolen from outside a gym in Glen Waverley at about 5pm on September 21. Police say the vehicles were subsequently driven through Melbourne's bayside and south-eastern suburbs.

A number of alleged robberies involving mostly lone women were reported on the evening of September 24.

At approximately 7:45pm, police allege a 64-year-old woman was dragged by several offenders while waiting at traffic lights outside Chadstone Shopping Centre. Her groceries were allegedly stolen.

A short time later, another woman was allegedly punched in the face and had her designer purse stolen at the same shopping centre.

Police also allege that shortly after 8pm, a woman was pushed to the ground and had her bag stolen on the Princes Highway in Clayton. Another alleged robbery occurred on Bluff Road in Highett, where a woman's handbag was reportedly stolen as she left a hairdresser.

Later that evening, at about 8:40pm, police allege offenders armed with a machete chased a male convenience-store worker on Bluff Road in Black Rock before stealing cash.

Detectives are also investigating whether the same group was responsible for other alleged bag thefts in Highett and Beaumaris.

The three males were arrested after police executed three search warrants at properties in Springvale and the Greater Dandenong area. An 18-year-old from Springvale was remanded in custody after being charged with multiple offences, including aggravated burglary, car theft and theft.

One 16-year-old has been released on bail after being charged with car theft and handling stolen goods, while the other remains in custody facing several charges.

Police said investigations are continuing and that charges have not been laid in some of the alleged robberies.

Authorities are appealing for witnesses and anyone with relevant footage to contact Crime Stoppers.

The allegations will be tested through the court process, and the accused people are entitled to the presumption of innocence.