Injection Moulding of flexible parts
There are several thermoplastic elastomers (TPE's) that can be easily processed by injection moulding and these offer a wide variety of hardness's. One of the best known trade names being Santoprene, see www.matweb.com
When prototyping, or undertaking short runs it is frequently possible to simplify the tool as the material can be deformed to cater for small undercuts and other features that on a hard material would require side actions. This same ductility can make the ejection of a part more difficult as the part will deform instead of leaving the tool.
Material selection is a subject in its own right and the best general advice is to (a) ensure the desired grade is available where the moulding is being undertaken, (b) preferably by a moulder with experience of that material family, and (c) utilise online resources such as Matweb to ensure the correct material properties are achieved.
Full details for this process can be viewed on the injection moulding of plastic parts page.