This study presents a novel methodology for analyzing blood flow features within small tubes, accounting for the unique geometries of flexible red blood cells, characterized by prolate and oblate shapes. The model incorporates a thin layer of lubricating fluid between the cell and the tube wall, simulating physiological conditions more accurately. Motivated by the challenges posed by the movement of red blood cells through narrow vessels, the effects of asymmetry and tube porosity are carefully examined. By solving the equations of motion and continuity analytically, employing boundary and matching conditions, we derive insights into the complex dynamics of blood flow. The proposed model’s results are compared against existing findings, revealing significant advancements in understanding flow characteristics. Graphical representations generated using MATLAB elucidate relationships among flow parameters, cell compliances, and slip effects. These relationships offer valuable insights into the intricate interplay between fluid dynamics and cellular mechanics within microcirculatory systems, contributing to the broader understanding of hemodynamics and its implications for health and disease.