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Climbing plants exhibit specialized shoots, called "searchers", to cross spaces and alternate between spatially discontinuous supports in their natural habitats. To achieve this task, searcher shoots combine both primary and secondary growth processes of their stems in order to support, orientate and explore their extensional growth into the environment. Currently, there is an increasing interest in developing models to describe plant growth and posture. However, the interactions between the sensing activity (e.g. photo-, gravi-, proprioceptive sensing) and the elastic responses are not yet fully understood. Here, we aim to model the extension and rigidification of searcher shoots. Our model defines variations in the radius (and consequently in mass distribution) along the shoot based on experimental data collected in natural habitats of two climbing species: Trachelospermum jasminoides (Lindl.) Lem. and Condylocarpon guianense Desf.. Using this framework, we predicted the sensory aspect of a plant, that is, the plant's response to external stimuli, and the plant's proprioception, that is, the plant's "self-awareness". The results suggest that the inclusion of the secondary growth in a model is fundamental to predict the postural development and self-supporting growth phase of shoots in climbing plants.