In [J. Reine Angew. Math. 626, 1–37 (2009; Zbl 1161.53020)], the authors have defined the holonomy groupoid of any singular foliation \({\mathcal F}\) on a smooth manifold \(M\), the convolution algebra of “smooth compactly supported” functions on this groupoid and the full and reduced \( C^*\)-algebra of the foliation. In the present paper, they construct the longitudinal pseudodifferential calculus for these foliations. The longitudinal differential operators are generated by vector fields along the foliation, whereas the pseudodifferential operators are obtained as images of distributions on bi-submersions with “pseudo-differential singularities” along a bisection. This construction is presented in the third section, where it is also shown that pseudodifferential operators have a principal symbol which is a homogeneous function on the subset of non-zero elements of “the cotangent space” \({\mathcal F}^*\) and that they form a \(\ast\)-algebra. Then, they show that the longitudinal pseudodifferential calculus has the classical ellipticity properties and that it allows for the Laplacian of a singular foliation to be realized as a self adjoint element of \(B (L^{2}(M))\). Several definitions from the previous paper, necessary for the undertsanding of this construction, are recalled. Interesting examples and outlines for future studies are also presented.