We investigate the critical properties of the Ising S=1/2 and S=1 model on
(3,4,6,4) and (3^{4},6) Archimedean lattices. The system is studied through the extensive
Monte Carlo simulations. We calculate the critical temperature as well as the critical
point exponents γ/ν, β/ν, and ν basing on finite size scaling analysis. The calculated
values of the critical temperature for S=1 are k_{B}T_{C}/J=1.590(3), and k_{B}T_{C}/J=2.100(4)
for (3,4,6,4) and (3^{4},6) Archimedean lattices, respectively. The critical exponents β/ν,
γ/ν, and 1/ν, for S=1 are β/ν=0.180(20), γ/ν=1.46(8), and 1/ν=0.83(5), for (3,4,6,4)
and 0.103(8), 1.44(8), and 0.94(5), for (3^{4},6) Archimedean lattices. Obtained results
differ from the Ising S = 1/2 model on (3,4,6,4), (3^{4},6) and square lattice. The evaluated
effective dimensionality of the system for S =1 are D_{eff} =1.82(4), for (3,4,6,4),
and D_{eff}=1.64(5) for (3^{4},6).