The development of practical lithium oxygen batteries with high specific energy needs to move towards the use of thick positive electrodes. However, a specific textural design of thick electrodes is required to enhance O2 diffusion which represents a significant limiting factor of the cell capacity. In this work we investigate, through a continuum modeling approach, the feasibility of using a bi-porous cathode to improve electrochemical cell response. This electrode contains mesopores providing active surface area towards the Oxygen Reduction Reaction (ORR) and macropores acting as an oxygen reservoir and diffusion medium. Results of this work highlight the complex interplays between the formulation, thickness and texture of the electrode as well as their impacts on the electrochemical performance.