We consider the effect of non-cylindrical axonal shape on axonal diameter mapping with diffusion MRI. Practical sensitivity to axon diameter is attained at strong diffusion weightings , where the deviation from the scaling yields the finite transverse diffusivity, which is then translated into axon diameter. While axons are usually modeled as perfectly straight, impermeable cylinders, the local variations in diameter (caliber variation or beading) and direction (undulation) have been observed in microscopy data of human axons. Here we quantify the influence of cellular-level features such as caliber variation and undulation on axon diameter estimation. For that, we simulate the diffusion MRI signal in realistic axons segmented from 3-dimensional electron microscopy of a human brain sample. We then create artificial fibers with the same features and tune the amplitude of their caliber variations and undulations. Numerical simulations of diffusion in fibers with such tunable features show that caliber variations and undulations result in under- and over-estimation of axon diameters, correspondingly; this bias can be as large as 100%. Given that increased axonal beading and undulations have been observed in pathological tissues, such as traumatic brain injury and ischemia, the interpretation of axon diameter alterations in pathology may be significantly confounded.