Recent studies show that several metal oxides and dichalcogenides (MX2), which exist in nature, can be stable in two-dimensional (2D) form and each year several new MX2 structures are explored. The unstable structures in H (hexagonal) or T (octahedral) forms can be stabilized through Peierls distortion. In this paper, we propose new 2D forms of RuS2 and RuSe2 materials. We investigate in detail the stability, electronic, magnetic, optical, and thermodynamic properties of 2D RuX2 (X = S, Se) structures from first principles. While their H and T structures are unstable, the distorted T structures (T'-RuX2) are stable and have a nonmagnetic semiconducting ground state. The molecular dynamic simulations also confirm that T'-RuX2 systems are stable even at 500 K without any structural deformation. T'-RuS2 and T'-RuSe2 have indirect band gaps with 0.745 eV (1.694 eV with HSE) and 0.798 eV (1.675 eV with HSE) gap values, respectively. We also examine their bilayer and trilayer forms and find direct and smaller band gaps. We find that AA stacking is more favorable than the AB configuration. The new 2D materials obtained can be good candidates with striking properties for applications in semiconductor electronic, optoelectronic devices, and sensor technology.