Abstract Flame instabilities in 2-methylfuran (MF) outwardly propagating laminar flames have been investigated experimentally and theoretically at the initial pressures of 1–4 bar, temperatures of 363–423 K and equivalence ratios of 0.7–1.4. The flame topography and the effects of flame instability on MF burning speeds have been examined. Flame instabilities start to develop and grow when cell evolution begins to appear on the flame surface and leads to the rebirth of new cells. These instabilities cause an incessant increment in the flame speed. Using the constant volume method (CVM) cellular burning speeds of MF spherically expanding flames were estimated. The cellular burning speeds showed oscillatory phenomena owing to the amplification of the growth rate of perturbation. However, the escalation of flame perturbation is somehow interrelated to the changes in the flame morphology. Consequently, the flame propagates at a constant acceleration rate at a hydrodynamic cut-off point and beyond. The theoretical linear stability model which is valid for variable transport properties has been used to determine the growth/decay rate of the unstable wavelengths of MF flames perturbation over a wide range of equivalence ratios. The critical conditions (critical radius and Peclet number) at which the flame becomes instable were determined from MF marginal stability curves. From the stability analysis, the critical Peclet number was somehow insensitive to initial pressure albeit the onset of instability was somewhat delayed at the initial temperatures. The critical radius and Peclet number decreased with increasing equivalence ratio in both the experiment and theoretical analysis. However, the experiment and the theoretical critical radius and Peclet number showed some discrepancies.