  We study the effects of the initial state radiation on the $s$-channel Higgs
boson resonant production at $\mu^+\mu^-$ and $e^+e^-$ colliders by convoluting
with the beam energy spread profile of the collider and the Breit-Wigner
resonance profile of the signal. We assess their impact on both the Higgs
signal and SM backgrounds for the leading decay channels $h\rightarrow b\bar
b,\ WW^*$. Our study improves the existing analyses of the proposed future
resonant Higgs factories and provides further guidance for the accelerator
designs with respect to the physical goals.
