The envelope is the shell of the tie and can be made from just about any fabric or material. The most common quality fibres are silk, linen, wool and cotton. You can also find some envelopes that are a blend of those fabrics, e.g. silk and wool.
A good quality tie is made of an envelope that was cut on the true bias, which is at 45 degrees from the finished edge of the fabric. When the envelope is not cut in this manner, the tie will not hang straight, or achieve its true elasticity. It will not withstand typical use and become permanently deformed.