Solid-oxide fuel cell (SOFC) are among the highest types of fuel cells in terms of efficiency, reaching as high as 65%. However, poor mechanical robustness and thermal cycling stability are the major disadvantages of these fuel cells due to high thermal stresses between layers. A new concept of a micro-monolithic ceramic cell was previously introduced that had extremely high power-densities (> 10 W/cm3) as well as high mechanical robustness and thermal cycling stability. In this study, a 3D comprehensive theoretical model is presented for ceramic fuel cells, which includes species, charge, momentum, and energy transport. Moreover, the bilinear elastoplastic material model is used to estimate thermal stresses in ceramics at high temperatures. This model is then used to simulate two new geometries for the cell and anode flow channels. Results indicate that circular anode channels are best in terms of thermal stresses, while being inferior in terms of electrochemical performance. A hexagonal cell with trapezoidal flow channels yielded the highest volumetric power density with an increase of 15% compared to the plain circular arrangement. On the other hand, circular sector flow channel increased the power density by only 9%. The increased current of the cell with the circular sectors and trapezoidal sections is due to the more efficient distribution of flow channel area such that the travel path for hydrogen gas is less restricted in terms of diffusion. As for the thermal stress, the newly introduced configurations increased the values of stress by 64% for the circular sector channels, compared to only 16% for the trapezoidal flow channels. This study is meant as an initial step in the optimization process for the microtubular SOFC with high volumetric power density, creating an opportunity for performance enhancement of this type of fuel cell.