We investigate in detail the processes involved when soft polymeric materials are imaged with TappingMode atomic force microscopy (TM-AFM). Measuring lateral arrays of amplitude/phase vs distance (APD) curves, we are able to determine quantitatively the amount of tip indentation and reconstruct the;shape of the "real" surface of the sample. Moreover, contrast inversion in height and TappingMode phase images is explained on the basis of attractive and repulsive contributions to the tip-sample interaction. The experiments are performed on surfaces of poly(styrene-block-butadiene-block-styrene) (SBS) triblock copolymers acting as a model system.