The cone loading tests (CLT/CLT-u) are an innovative alternative to the conventional CPT test, allowing the measurement of soil stiffness. This paper aims to present the results of an experimental study of the (CLT/CLT-u) within the framework of physical modelling at natural gravity by using the calibration chamber. This technique makes it possible to carry out a full-scale penetration test within a soil slice. After describing the experimental devices and the loading program, the paper will focus on the presentation and discussion of the results of cone penetration (CPT) and cone loading (CLT) tests in Fontainebleau sand and Speswhite Kaolinite clay. Experimental load-transfer curves were then derived, and their parameters were determined. It was found that the cone modulus and the friction stiffness linearly increase with depth, according to the model of Gibson’s soils. Comparison with the conventional soil properties of the soils tested led to the conclusion that these parameters may be used for a practical characterization of the soil stiffness.