Isolation module between a vibration-generating device, such as a satellite launcher, and a structure to be isolated, such as the structure carrying a satellite, comprising: - at least two fastening parts ( 4, 5) intended to be fastened respectively on the vibration-generating device and the structure to be isolated, - connecting means made from elastomer material interposed between the two fastening parts, allowing at least one degree of freedom in translation along a longitudinal axis between the two fastening parts, - a first fastening part, called a frame comprises at least two parallel radial branches ( 7, 7', 8, 8') called lower and upper, at a distance from each other along the longitudinal axis, and the second fastening part, called the support, comprises at least one radial branch ( 9, 9') called the median branch, extending between the two branches ( 7, 7', 8, 8') of the frame, the two radial branches ( 7, 7', 8, 8') of the frame being symmetrical with each other with respect to a plane perpendicular to the longitudinal axis, - the elastomer connecting means comprise at least one pair of identical elastomer pads ( 13, 13', 14, 14'), in which each pad ( 13, 13', 14, 14') extends along the longitudinal axis between a first end ( 15, 16) and a second end ( 17, 18), a first pad ( 13, 13') having the first end supported on a lower branch ( 7, 7') of the frame and the second end supported on the median branch of the support and the second pad ( 14, 14') having the first end supported on the upper branch of the frame and the second end supported on the median branch of the support, the two pads ( 13, 13', 14, 14') of the pair being thus mounted in parallel between the frame and the support and being active along the longitudinal axis in opposite directions, so that when one pad works under tension, the other pad of the pair works under compression, and vice-versa, - the stiffness of the module being symmetrical, whether a force applied thereto along the longitudinal axis is oriented in one direction or the opposite direction, the module being characterized in that - each pad ( 13, 13', 14, 14') is dimensioned so that the contact surface of one end ( 15, 16, 17, 18) in contact with a radial branch ( 7, 7', 8, 8', 9, 9') and the free contact surface satisfy the relationship: S 1 S 2 ≤ 3. - at least two fastening parts ( 4, 5) intended to be fastened respectively on the vibration-generating device and the structure to be isolated, - connecting means made from elastomer material interposed between the two fastening parts, allowing at least one degree of freedom in translation along a longitudinal axis between the two fastening parts, - a first fastening part, called a frame comprises at least two parallel radial branches ( 7, 7', 8, 8') called lower and upper, at a distance from each other along the longitudinal axis, and the second fastening part, called the support, comprises at least one radial branch ( 9, 9') called the median branch, extending between the two branches ( 7, 7', 8, 8') of the frame, the two radial branches ( 7, 7', 8, 8') of the frame being symmetrical with each other with respect to a plane perpendicular to the longitudinal axis, - the elastomer connecting means comprise at least one pair of identical elastomer pads ( 13, 13', 14, 14'), in which each pad ( 13, 13', 14, 14') extends along the longitudinal axis between a first end ( 15, 16) and a second end ( 17, 18), a first pad ( 13, 13') having the first end supported on a lower branch ( 7, 7') of the frame and the second end supported on the median branch of the support and the second pad ( 14, 14') having the first end supported on the upper branch of the frame and the second end supported on the median branch of the support, the two pads ( 13, 13', 14, 14') of the pair being thus mounted in parallel between the frame and the support and being active along the longitudinal axis in opposite directions, so that when one pad works under tension, the other pad of the pair works under compression, and vice-versa, - the stiffness of the module being symmetrical, whether a force applied thereto along the longitudinal axis is oriented in one direction or the opposite direction, the module being characterized in that - each pad ( 13, 13', 14, 14') is dimensioned so that the contact surface of one end ( 15, 16, 17, 18) in contact with a radial branch ( 7, 7', 8, 8', 9, 9') and the free contact surface satisfy the relationship: S 1 S 2 ≤ 3.