Plasma sources based on flexible substrates are receiving attentions for their unique adaptability to irregular surfaces and large range of plasma coverage, which brings them irreplaceable advantages in the fields of material processing and biomedical treatment. Plenty studies have been carried out focusing on the application effects of these flexible plasma sources, while their surface discharge characteristics and mechanisms still lack revelation. In this work, a flexible plasma sheet with the structure of surface dielectric barrier discharge is realized through printed circuit board, and its multiple surface ionization waves (SIWs) propagation on curved gas-solid interfaces is studied by experiments and 2D fluid simulation models. Qualitative agreement is achieved between the experiments and simulations. It is found that a positive and a negative discharge generate at the rising and falling edge of the excitation pulse, respectively. In the positive discharge, SIWs originate at the grounded mesh edge and then propagate to the center in a petal-like pattern, which is shaped by the space electric field. Controlled by electron collision reactions, developments of the excited states for N2 and O2 molecules are similar to that of electrons. In the negative discharge, electrons dissipate and no SIW is generated. The evolutions of heavy particles show differences in this period, which is attributed to the disparate rate coefficients of their consumption reactions. Further study shows that when the plasma sheet turns from convex to concave, the electron density and electron temperature above its surface increase, but the petal patterns of SIWs propagation have no variation. The electron density, electron temperature, and electron impact ionization source will rise as a result of the increasing pulse amplitude or the decreasing duration of the pulse rising edge.