In Arabidopsis thaliana , successful fertilization relies on the precise guidance of the pollen tube tip as it navigates through the female pistil tissues to deliver non-motile sperm cells to ovules. While prior studies have unveiled the role of the pistil in directing pollen tubes to ovules, growth guidance mechanisms within the stigmatic epidermis during the initial phase of the pollen tube’s journey remains elusive. A recent analysis comparing wild-type (WT) pollen tube paths in WT and ktn1-5 stigmatic cells revealed a tight connection between directed pollen tube growth and the mechanical properties of the invaded stigmatic cell. Building upon these observations, we constructed here a mathematical model to explore the mechanisms guiding early pollen tube growth through the papilla cell wall (CW). We found that in ktn1-5 , the pollen tube moves freely on the curved papilla surface, following geodesics, while the WT papilla exerts directional guidance on the pollen tube. An order of magnitude analysis of the mechanical forces involved in pollen tube growth in papillae suggests a guidance mechanism, where the elongated papilla geometry and the CW elasticity combine to efficiently direct pollen tube growth towards the papilla base.