Fast fashion primarily relies on non-renewable resources, particularly synthetic fibres, during its production processes. Here are a few examples:

1. Polyester: This is the most commonly used fibre in clothing, largely due to its durability, water-resistance, and wrinkle-free properties. However, polyester is made from crude oil, a non-renewable resource. Its production process is energy-intensive, releasing harmful pollutants and contributing significantly to global warming.

2. Nylon: Initially designed as a substitute for silk, Nylon is another petroleum-based synthetic fibre. The production of nylon involves a great deal of energy and releases nitrous oxide, a potent greenhouse gas. 

3. Acrylic: This synthetic fibre, used as a substitute for wool, is also derived from fossil fuels. Its production involves highly toxic substances and releases large amounts of hazardous pollutants.

4. Elastane (also known as Spandex or Lycra): Loved for its elasticity, elastane is a synthetic fibre made from polyurethane, a polymer derived from petroleum. It's widely used in fast fashion for its stretchability but its production, like other synthetics, involves non-renewable resources and results in environmental pollution.

5. Rayon (including Modal and Viscose): While technically derived from renewable cellulose (often from wood pulp), the chemically-intensive process to produce these fabrics often involves carbon disulphide, a toxic substance linked to numerous health and environmental issues. While there are better-managed and more sustainable versions of these fibres available (such as Tencel), they're seldom used in fast fashion due to the higher cost.

In conclusion, despite the cost and convenience benefits these materials offer to the fast fashion industry, their environmental impact from the extraction, processing and disposal stages is highly damaging. Transitioning towards more sustainable, renewable resources is a necessary step for the industry's future.