  We estimate the mass accretion rate (MAR) of the 346 clusters of galaxies in
the HectoMAP Cluster Survey. The clusters span the redshift range $0.17-0.42$
and the $M_{200}$ mass range $\approx (0.5 - 3.5)\cdot 10^{14} M_\odot$. The
MAR estimate is based on the caustic technique along with a spherical infall
model. Our analysis extends the measurement of MARs for 129 clusters at $z<0.3$
from the Cluster Infall Regions in the Sloan Digital Sky Survey (CIRS) and the
Hectospec Cluster Survey (HeCS) to redshift $z \sim 0.42$. Averaging over
redshift, low-mass clusters with $M_{200}\sim 0.7\cdot 10^{14} M_\odot$ accrete
$\sim 3\cdot 10^4 M_\odot$yr$^{-1}$; more massive clusters with $M_{200}\sim
2.8\cdot 10^{14} M_\odot$ accrete $\sim 1\cdot 10^5 M_\odot$yr$^{-1}$. Low- and
high-mass clusters increase their MAR by $\sim 46\%$ and $\sim 84\%$,
respectively, as the redshift increases from $z\sim 0.17-0.29$ to $z\sim
0.34-0.42$. The MARs at fixed redshift increase with mass and MARs at fixed
mass increase with redshift in agreement with $\Lambda$CDM cosmological model
for hierarchical structure formation. We consider the extension of MAR
measurements to $z \sim 1$.
