This paper refers to cyclic shear strains (γc) and permanent shear strains (γp) of a soft cohesive soil, when both monotonic shear stresses (τo) and cyclic shear stresses (τc) are applied. The research is backed by an extensive experimental program with 139 cyclic simple shear tests that included identification and classification tests. These cyclic simple shear tests were conducted under different levels of stresses, τo, before the cyclic phase. Laboratory tests were carried out on undisturbed samples from the Port of Barcelona, located in Spain on the Mediterranean coast, and characterized by a monotonic strength (τmax) approximately equal to 30% of the initial effective vertical stress (σ′ov). The samples were taken at depths between 29 and 52 m and correspond to an initial effective vertical stress between 277 and 413 kPa, respectively. In general, the results indicate that: (a) the combination of τo and τc controls the generation of γc and γp, (b) it is not always true that when τo/σ′ov + τc/σ′ov ≈ τmax/σ′ov, the soil reaches failure cyclically, and (c) empirical relations useful for design can be established between γc, γp, and the number of cycles (N), for different relationships varying (τo/σ′ov) between 0% and 25%.