The immediate undrained poroelastic response after drilling is critical for short-term wellbore stability in low-permeability formations. Despite its significance, existing analytical undrained wellbore stress solutions in transversely isotropic formations are limited to special cases where the borehole axis is either perpendicular or parallel to the plane of transverse isotropy. By extending Amadei's elastic framework into the undrained poroelastic regime, this study presents an analytical undrained solution for arbitrarily inclined boreholes in transversely isotropic formations, considering fully anisotropic undrained poroelastic effects. Validation against undrained isotropic and transversely isotropic solutions, as well as anisotropic Biot's effective stress coefficients, demonstrates the robustness of the proposed model. The derived Biot's effective stresses are subsequently applied to evaluate short-term collapse pressure with varying wellbore trajectories. Results show that undrained wellbore stress distributions deviate significantly from drained Amadei solution with varying elastic property anisotropy and wellbore pressure, particularly in terms of axial and shear stress components. Furthermore, estimating the undrained pore pressure response using drained Amadei stress solution introduces substantial errors, highlighting the necessity of adopting a fully anisotropic undrained poroelastic framework. Unlike isotropic formations, the anisotropic undrained pore pressure response exhibits an asymmetrical distribution, reflecting coupled shear-tension and solid-fluid couplings. Polar plots of collapse pressure that incorporate the undrained effect exhibit significant differences compared to those derived from previous models, indicating that the optimal drilling direction may not coincide with the orientation of the horizontal principal stress. This analytical solution establishes a benchmark for fully anisotropic undrained wellbore stress distribution and holds substantial implications for enhancing early-stage wellbore stability assessments in strongly anisotropic poroelastic formations.