In global gravity forward modelling the tesseroid is commonly used as elementary mass element. However, formulas for the gravitational potential and its derivatives currently suffer from numerical problems when evaluating in its close proximity. Based on the subdivision of a tesseroid in smaller rectangular prisms, this study examines the gravitational field in the close proximity of a tesseroid including its faces, edges, vertices and interior and quantifies approximation errors when replaced by a single rectangular prism. Results show that approximation errors can exceed 100 μGal when placing the computation point at the vertex of a 30 × 30 ×10 km tesseroid but considerably reduce for smaller tesseroids and when placing the computation point at the tesseroid’s centre top face. While this study confirms that the prism is a suitable mass element to model masses in close proximity of the evaluation point it also opens further research questions.