The steady and unsteady 2D flows around the airfoil were analyzed by utilizing the vortex singularity elements with two different inviscid flow models. Firstly, the steady flow was modeled in the light of steady state algorithm available in the literature. Then, the unsteady flow model was developed by some modifications on the algorithm of the steady flow. All the algorithms were transformed to the code in MATLAB® 2018a environment. For the steady state model, lift coefficients were compared with the inviscid and inviscid-viscous coupling models of the Xfoil 6.9 program data (Drela, 2001); and NASA experimental archive (Ira Herbert Abbott & Von Doenhoff, 1959). Since the model is inviscid, the reference point is the inviscid solvers; and the model agreed well with the Xfoil 6.9 inviscid mode for different type of airfoils. The unsteady model was created with three different operating modes; which are the sudden forward, heaving and the pitching. For the sudden forward motion, the lift and drag coefficients were compared with the studies in the literature. Besides, the lift, drag moment coefficients; and the wake patterns of the heaving and pitching motions were compared with the experimental data in the literature. The model is limited in terms of reflecting lift, drag and moment coefficients due to the not being included the viscous effects, flow separation, stall etc.; however, in terms of capturing the wake patterns, the model is quite useful.