The human spine plays a fundamental role in providing support and flexibility to the torso during posture and locomotion. During growth, changes in vertebral size and shape can influence spinal alignment and increase the risk of pathologies such as adolescent idiopathic scoliosis. Experimental investigation of spinal growth in humans is challenging, as it would require long-term imaging of paediatric populations, raising ethical and health concerns. Numerical simulations therefore represent a valuable alternative to investigate the mechanisms driving vertebral growth. In this work, we describe a computational framework for modelling vertebral growth by combining a statistical shape model (SSM) of lumbar vertebrae derived from a paediatric population with a bulk growth model based on generalised continuum mechanics. An inverse methodology is introduced to extrapolate heterogeneous vertebral growth fields from SSM based on experimental data and apply them within finite element simulations. The framework is demonstrated on the L4 vertebra, where numerical predictions show excellent agreement with experimental measurements of key morphological parameters. While the SSM captures surface displacements, the finite element approach enables a full description of internal mechanical and growth fields, providing a basis for realistic simulations of vertebral growth.