A resilient sleeve for a beverage container is made from a continuous web of a fabric extending between distal and proximal ends thereof. A substantially linear base is provided at the proximal end. First and second sides extend outwardly from the opposite ends of the base. Two substantially symmetrical trapezoidal regions are formed at the distal end of the web, wherein each trapezoidal region is formed by an outer side positioned at a first predetermined angle to the first side and an inner side positioned at a second predetermined angle to a longitudinal axis of the web portion. A V-shaped cut out portion is formed at a central area of the web by the inner sides of the first and second trapezoidal regions. Width of the web portion corresponds to a circumference of the sleeve and length of the web portion corresponds to an axial length of the sleeve.