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. Plant growth is influenced by many external and internal factors, such as light, gravity, structural flexibility of the stem or hormone fluxes. In recent years, plant movements and modelization have received an increasing attention, leading to a better understanding of plant development. In this work, we introduce a 2D model for self-supporting structures developed by climbing plants. This model is in the direction of filling the gap that currently exists between models for plant sensing activity and models focused on the mechanical aspect of plant growth. Indeed, we consider the response of the plant to external cues together with the capability of the plant to perceive itself (proprioception) and the radial expansion process (secondary growth). We then see how to retrieve the model parameters from a minimal set of experimental data and finally test the model by comparing its numerical simulations with real plant shapes. Our result shows that a better consideration of mass distribution along the shoot is important to understand the shape of self-supporting structures.