The paper presents the results of measurements the specific concentration of lead-210 for six peat profiles representing four peat bogs from two regions of Poland and the problem of creating age-depth models. For the construction of age-depth models, it is proposed to use mathematical functions, the best fit to the measured activity. The F-statistics were used as a measure of the match quality. The obtained models are visualized in two ways–showing the age calculated on the basis of direct measurements of activity and indicating points that are the results of the used approximation. Such visualization is important to clearly distinguish the places of the age-depth model that result from the measurements of activity from those places that are the result of the approximation used. This paper proposes and tests the application of activity modelling for the cores shorter than the range of the lead method. The paper also outlines the limitations and potential dangers related to the interpretation of core dating results i) obtained by using the activity approximation resulting in the smoothing of the age-depth profile, and ii) for the cores of a length smaller than the depth of the presence of the unsupported lead.