The tear strength of thermoset rubbers, thermoplastic elastomers, and silicones can be measured according to specification ASTM D624. The test measures the strength required to initiate a tear in a material. D624 describes multiple different types of sample shapes that can be tested in a standard universal testing machine (tensile testing machine). Usually materials that are tested to D624 are also tested according to specification ASTM D412 to measure the tensile strength and elongation. If you are going to perform this test, you should read the entire specification from ASTM. This is a quick summary to decide if this test is right for you, and to point out what equipment you need to perform the test.
This video shows how to perform a tear strength test: