Abstract A general framework to develop incrementally non-linear constitutive relations is given. In this constitutive theory it is needless to define plastic potential surfaces and yield functions which are very difficult to exhibit experimentally in a consistent manner. An incrementally non-linear of second order model which belongs to that class of constitutive relations is presented and applied to the simulation of triaxial tests carried out on a normally consolidated kaolin. Drained tests were utilized to calibrate the constitutive relations whereas axisymmetrical and threedimensional undrained tests permitted to study the validity of the model. Some comments in relation with the International Workshop on Constitutive Relations for Soils (Grenoble, 1982) are given and a constitutive instability is discussed.