In this paper, the class of $(p,q)$-Bessel-Appell polynomials is introduced. The generating function, series definition and determinant definition of this class are established. Certain members of $(p,q)$-Bessel-Appell polynomials are considered and some properties of these members are also derived. Further, the class of 2D $(p,q)$-Bessel-Appell polynomials is introduced by means of the generating function and series definition. In addition, the graphical representations of some members of $(p,q)$-Bessel-Appell polynomials and 2D $(p,q)$-Bessel-Appell polynomials are plotted with the help of Matlab.