Beam instabilities due to High Order Modes (HOMs) are a concern to superconducting (SC) linacs such as the Spallation Neutron Source (SNS) linac. The effects of pulsed mode operation on transverse and longitudinal beam breakup instability are studied for H− beam in a consistent manner for the first time. Numerical simulation indicates that cumulative transverse beam breakup instabilities are not a concern in the SNS SC linac, primarily due to the heavy mass of H− beam and the HOM frequency spread resulting from manufacturing tolerances. As little as ±0.1 MHz HOM frequency spread stabilizes all the instabilities from both transverse HOMs, and also acts to stabilize the longitudinal HOMs. Such an assumed frequency spread of ±0.1 MHz HOM is small, and hence conservative compared with measured values of σ=0.00109(fHOM−f0)/f0 obtained from Cornell and the Jefferson Lab Free Electron Laser cavities. However, a few cavities may hit resonance lines and generate a high heat load. It is therefore prudent to have HOM dampers to avoid the danger of quenching a cavity.