  This study explores the primary effects of dielectric materials in a resonant
cavity-based search for axion dark matter. While dielectrics prove beneficial
in numerous cases, their incorporation may lead to less-than-optimal
performance, especially for the lowest TM mode. Additionally, the stronger
confinement of the electric field inside the dielectrics can exacerbate mode
mixings, in particular for higher-order modes. Case studies have been carried
out using a combination of analytical solutions and numerical simulations. The
findings indicate dielectric cavities employing the $\text{TM}_{010}$ mode
experience a significant reduction in sensitivity when compared to a similar
search conducted in a cavity at equivalent frequency using no dielectrics.
