We explore new analytical solutions for the two-dimensional nonlinear elliptic Bratu equation. Through the point transformation, the integrable form of Bratu equation was investigated then we obtain the Lie infinitesimals for the new equation. These vectors reduce the integrable equaation to solvable ODEs then we use the boundary conditions (BCs) to spin two new exact solutions for Bratu equation in a unit square domain. A three-dimensional plot illustrates some resulting solutions. Comparison with other work has been presented.