Significance The discovery of MXenes opens an opportunity on flexible energy storage. We explored systematically several factors including metal species, layer thicknesses, functional group, strain, and Li concentration on the mechanical and electrochemical properties of 2D transition metal carbides (TMCs). Taking the electrode polarization into account, we found several critical factors that govern the ionic mobility on the surface of 2D TMCs. Under multiaxial loadings, the electrical conductivity, high ionic mobility, low equilibrium voltage with good stability, excellent flexibility, and high theoretical capacity offered bare 2D TMCs the potential to be ideal flexible anode materials, whereas the surface functionalization degraded the transport mobility and increased the equilibrium voltage. General rules are proposed to identify the optimal candidate based on a combined analysis of these critical parameters.