A capsule for making a drink comprises a cup-shaped main body (6) forming a housing chamber (7) containing a powdered or liquid substance (2). The main body (6) comprises a bottom wall (8) and a lateral wall (9) which has a lower portion (10) connected to the bottom wall (8) and an upper portion (11) delimiting an opening which is closed by a cover element (17). The capsule also comprises lengthening means (18) which, following an increase in the capsule (1) internal pressure, allow a movement away from the cover element (17) by the lower portion (10) of the lateral wall (9) and the bottom wall (8) connected to it. Also claimed is a method which comprises feeding water and/or steam into the capsule (1) to increase the capsule (1) internal pressure and so cause the movement of the lower portion (10) of the lateral wall (9) and the bottom wall (8) away from the cover element (17) until the bottom wall (8) is torn against external piercing means, thus allowing the drink to be supplied through the bottom wall (8).
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