A cannula device for infusion sets is provided. The cannula device includes a housing and at least one membrane mounted to the housing and adapted for receiving a piercing member of a connector. The cannula device further includes a cannula mounted to the housing. The cannula device is adapted to removably attach to a base part of an infusion set. The cannula device can receive the piercing member from a first receiving direction and from a second receiving direction different from the first receiving direction, providing fluid communication between the piercing member and the cannula mounted to the housing.