  This article explores wormhole solutions within the framework of Finsler
geometry and the modified gravity theory. Modifications in gravitational
theories, such as $f(\mathcal{R}, \mathcal{T})$ gravity, propose alternatives
that potentially avoid the exotic requirements. We derive the field equations
to examine the conditions for Finslerian wormhole existence and investigate
geometrical and material characteristics of static wormholes using a polynomial
shape function in Finslerian space-time. Furthermore, we address energy
condition violations for different Finsler parameters graphically. We conclude
that the proposed models, which assume a constant redshift function, satisfy
the necessary geometric constraints and energy condition violations indicating
the presence of exotic matter at the wormhole throat. The results are validated
through analytical solutions and 3-D visualizations, contributing to the
broader understanding of wormholes in Finsler-modified gravity contexts.
