Recently, Group-V monolayer elements, especially the novel allotropes of arsenene and antimonene, have attracted significant attention. Motivated by this, we employed first principles to systemically investigate the properties of seven new allotropes of arsenene and antimonene. Through analysis of cohesive energy and phonon mode dispersion, we proved their high dynamical stability. Thermodynamics were also considered with Debye temperature, heat capacity and Gibb's free energy, which revealed their basic thermal properties and thermo-dynamic stability at ambient temperature. By calculating the band structures, we found that γ-type, δ-type, ε-type and ζ-type for both arsenene and antimonene are semiconductors with direct band gaps, but η-type, θ-type and ι-type for both arsenene and antimonene are semiconductors with indirect bandgaps. Furthermore, by studying optical absorptions, we discovered that these arsenene and antimonene allotropes exhibit absorption from visible to ultraviolet region with clear linear dichroism in x and y directions; particularly, γ-type and ζ-type have stronger optical absorption than others.