The presence of imperfections significantly reduces the load carrying capacity of thin cylindrical shells due to the high sensitivity of thin shells to imperfections. To nullify this unfavorable characteristic, thin cylindrical shells are designed using a conservative knockdown factor method, which was developed by NASA in the late 1960s. Almost all the design codes, explicitly or implicitly, follow this approach. Recently, a new approach has emerged to significantly reduce the sensitivity of thin cylindrical shells. In this approach, wavy cross sections are used instead of circular cross sections for creating thin cylinders. Past studies have demonstrated the effectiveness of wavy cylinders to reduce imperfection sensitivity of thin cylinders under axial compression assuming linear elastic material behavior. These studies used eigenmode imperfections which do not represent realistic imperfections found in cylinders. In this paper, using a realistic dimple-like imperfection, new insights are presented into the response of wavy cylinders under uniform axial compression and bending. Furthermore, the effectiveness of the wavy cylinders to reduce imperfection sensitivity under bending load is investigated assuming a plastic Ramberg–Osgood material model. The effect of wave parameters, e.g., the amplitude and the number of waves, is also explored. This study reveals that wavy thin cylinders are insensitive to imperfections under bending in the inelastic range of the material. It is also found that the wave parameters play a decisive role in the response of thin wavy cylinders to imperfections under bending.