We propose a novel one–dimensional model for morpho–poroelasticity. This model combines mechanical displacement with tissue growth or shrinkage. This tissue growth or shrinkage may be caused by biological processes such as secretion of collagen, cell proliferation or by micro-structural changes of the collagen phase. The central focus of our study revolves around a comprehensive linear stability analysis of the equilibrium state within the proposed model. This analytical approach allows us to assess the stability of the system under different perturbation conditions which is critical for predicting the behavior of the system over time and under various external influences. Additionally, numerical experiments are included to visually demonstrate the proposed concept.