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The cylindrical shape of soft-bodied invertebrates is well suited to functions in skeletal support and locomotion, but may result in a previously unrecognized cost—large non-uniformities in muscle strain and strain rate among the circular muscle fibres of the body wall. We investigated such gradients of strain and strain rate in the mantle of eight long-finned squid Doryteuthis pealeii and two oval squid Sepioteuthis lessoniana. Transmural gradients of circumferential strain were present during all jets (n = 312); i.e. for a given change in the circumference of the outer surface of the mantle, the inner surface experienced a greater proportional change. The magnitude of the difference increased with the amplitude of the mantle movement, with circular muscle fibres at the inner surface of the mantle experiencing a total range of strains up to 1.45 times greater than fibres at the outer surface during vigorous jets. Differences in strain rate between the circular fibres near the inner versus the outer surface of the mantle were also present in all jets, with the greatest differences occurring during vigorous jetting. The transmural gradients of circumferential strain and strain rate we describe probably apply not only to squids and other coleoid cephalopods, but also to diverse soft-bodied invertebrates with hollow cylindrical or conical bodies and muscular organs.