Abstract In this paper, we perform the detailed modeling for the light curves (LCs) of PTF~10iuv
which is a calcium-rich (Ca-rich) supernova (SN) to constrain its physical properties
of the ejecta, the energy sources, as well as the explosion mechanism.
We find that the $^{56}$Ni model and
the $^{56}$Ni plus circumstellar interaction (CSI) model fail to explain the LCs, while
the four-element ($^{56}$Ni, $^{48}$Cr, $^{52}$Fe, and $^{44}$Ti) model can account for the LCs.
The ejecta mass of PTF~10iuv derived by the model ($1.52^{+0.34}_{-0.25}$ M$_\odot$)
is consistent with that of the merger of
sub-Chandrasekhar mass white dwarf.
The early-time LCs were mainly
powered by $^{56}$Ni whose mass is $\sim 0.03 $ M$_\odot$, 
while the contributions of $^{48}$Cr and $^{52}$Fe can be neglected.
The derived $^{44}$Ti mass ($\sim$ 0.25 M$_\odot$) is $\sim$ 1.8 times the upper limit
of the derived $^{44}$Ti mass of Ca-rich SN~2005E.
We suggest that subtracting the contributions of the host-galaxy which is unknown and
including the flux from other long-lived elements (e.g., $^{57}$Co, $^{55}$Fe, $^{60}$Co) can
reduce the amount of $^{44}$Ti, and that this value
can be regarded as an upper limit.