Staffordshire Police said the incidents were reported after people had been shopping in the town centre on Sunday 23 August.
Officers have not given details of where individual thefts took place or how many people are believed to have been targeted, but have issued advice urging shoppers to be particularly aware of their belongings.
Police said thieves can use distraction techniques, meaning victims may not realise anything has been taken until later.
Tactics can include deliberately bumping into someone, asking for directions or the time, or creating confusion in crowded areas while another person takes valuables.
Shoppers are being advised to keep handbags fastened and close to their body, with the opening facing inwards, and to keep a hand on their bag in busy areas.
Police also recommend avoiding keeping wallets, purses or mobile phones in back pockets, and not putting valuables in easily accessible parts of backpacks.
Bags should not be left attached to wheelchairs, mobility scooters, prams or pushchairs.
Staffordshire Police said the reported thefts are currently being investigated.
Anyone who sees suspicious activity can contact police on 101. In an emergency, call 999.
