An insulating device for a thermal and/or acoustic insulation of an exhaust system of a vehicle has a first half shell including at least a first connection rim and a second half shell including at least a second connection rim, the first half shell and the second half shell being connected by a welded joint at the connection rims. The connection rims are reshaped into a multiple fold. Further disclosed are a vehicle exhaust system having an exhaust gas-carrying duct and an insulating device circumferentially surrounding the duct, as well as a method for producing an insulating device for a thermal and/or acoustic insulation of an exhaust system of a vehicle.