After submission of the manuscript, the authors became aware of the paper "Existence results for a morphoelastic model" by Elisa Davoli, Katerina Nik, and Ulisse Stefanelli, ZAMM online first which investigates a closely related model in three dimensions with slightly restricted kinematics. Funding information Deutsche ForschungsgemeinschaftExistence and uniqueness of solutions for a class of models for stress-modulated growth is proven in one spatial dimension. The model features the multiplicative decomposition of the deformation gradient 𝐹 into an elastic part 𝐹 𝑒 and a growthrelated part 𝐺. After the transformation due to the growth process, governed by 𝐺, an elastic deformation described by 𝐹 𝑒 is applied in order to restore the Dirichlet boundary conditions and, therefore, the current configuration might be stressed with a stress tensor 𝑆. The growth of the material at each point in the reference configuration is given by an ordinary differential equation for which the right-hand side may depend on the stress 𝑆 and the pull-back of a nutrient concentration in the current configuration, leading to a coupled system of ordinary differential equations.