<p>This work presents novel three-dimensional solutions for coupled mechanical–electrical interactions in transversely isotropic porous-piezoelectric materials (PPEMs), grounded in Biot’s consolidation theory. By leveraging potential theory, operator theory, and Almansi’s theorem, we derive compact general solutions expressed through harmonic functions, satisfying both weighted harmonic and octaharmonic partial differential equations. Building on these solutions, we extend the analytical framework to solid cones subjected to axial and transverse forces, and point charges in both solid and fluid phases, addressing compression and bending scenarios. Numerical simulations, validated against existing literature, reveal key physical phenomena: rapid contour variations near sources, zero-field limits at greater distances, the influence of vertex angles on the distribution trend of coupled fields, and the concentration of coupled fields near points of action. These findings deepen the understanding of PPEMs, offering insights for applications in geotechnics, smart materials, and biomedical engineering, while paving the way for future innovations.</p>