Theoretical work and recent observations suggest that the dayside magnetopause may support its own eigenmode, consisting of propagating surface waves which reflect at the northern and southern ionospheres. These magnetopause surface eigenmodes (MSEs) are a potential source of magnetospheric ultralow‐frequency (ULF) waves with frequencies less than 2 mHz. Here we use the Space Weather Modeling Framework to study the magnetospheric response to impulsive solar wind dynamic pressure increases. Waves with 1.8 mHz frequency are excited whose global properties are largely consistent with theoretical predictions for MSE and cannot be explained by other known ULF wave modes. These simulation results lead to two key findings: (1) MSE can be sustained in realistic magnetic field geometries with nonzero flow shear and finite current layer thickness at the magnetopause and (2) MSE can seed the growth of tailward propagating surface waves via the Kelvin‐Helmholtz instability.Key PointsDayside ULF response to pulse consistent with magnetopause surface eigenmodeMagnetopause surface eigenmodes are a potential source of ULF waves below 2 mHzMagnetopause surface eigenmodes seed tailward propagating surface wave growthPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111803/1/grl52799.pd