  A new two-dimensional material, the C$_2$N holey 2D (C$_2$N-$h$2D) crystal,
has recently been synthesized. Here we investigate the strain effects on the
properties of this new material by first-principles calculations. We show that
the material is quite soft with a small stiffness constant and can sustain
large strains $\geq 12\%$. It remains a direct gap semiconductor under strain
and the bandgap size can be tuned in a wide range as large as 1 eV.
Interestingly, for biaxial strain, a band crossing effect occurs at the valence
band maximum close to a 8\% strain, leading to a dramatic increase of the hole
effective mass. Strong optical absorption can be achieved by strain tuning with
absorption coefficient $\sim10^6$ cm$^{-1}$ covering a wide spectrum. Our
findings suggest the great potential of strain-engineered C$_2$N-$h$2D in
electronic and optoelectronic device applications.
