This paper proposes a new condition for achieving robust finite-time stability (FTS) of two-dimensional (2D) linear systems in the continuous-continuous time-invariant setting. FTS is in its essence adapted to 2D systems since it ensures that, for a given bound on initial conditions, weighted norms of the vertical and horizontal state variables will not exceed a certain bound during a predefined time interval. On the basis of this concept a new and original control design problem, using the 2D FTS as a constraint, is proposed. In fact, a prominent parametric insensitive control design for LTI systems is recast here as an FTS control design for a specific 2D system. Moreover, the paper not only gives an extension of the 1D FTS concept to 2D systems but also proposes some extended LMI conditions, with a reduced conservatism, for achieving robust closed-loop FTS by means of a state-feedback. A numerical example is given to illustrate the effectiveness of the proposed conditions.