Abstract The subject of the paper comprises tests of cohesive soil subjected to low-frequency cyclic loading with constant strain amplitude. The main aim of the research is to define a failure criteria for cohesive soils subjected to this type of load. Tests of undrained cyclic shear were carried out in a triaxial apparatus on normally consolidated reworked soil samples made of kaolinite clay from Tułowice. Analysis of the results includes the influence of number of load cycles on the course of effective stress paths, development of excess pore water pressure and stress deviator value. Observed regularities may seem surprising. The effective stress path initially moves away from the boundary surface and only after a certain number of load-unload cycles change of its direction occurs and it starts to move consequently towards the surface. At the same time, it has been observed that pore water pressure value decreases at the beginning and after few hundred cycles increases again. It is a typical behaviour for overconsolidated soil, while test samples are normally consolidated. Additionally, a similar change in deviator stress value has been observed - at first it decreases and later, with subsequent cycles, re-increases.