The availability of closed-form solutions of problems dealing with discontinuous structures can be useful to perform sensitivity analyses with respect to the governing parameters or to infer inverse formulas to solve identification problems. Aiming at providing solutions for uncovered problems, this paper presents the closed-form expression of the static response of the Timoshenko circular arch in presence of multiple cracks. The presented approach represents an extension of a previous study devoted to the statics of inextensible multi-cracked Euler-Bernoulli arch, that was subsequently studied in the dynamic context. The framework is the Timoshenko theory accounting for the flexural and shear deformabilities as well as for the extensibility of the arch. Aiming at defining the governing equations over a unique domain in spite of the concentrated discontinuities, the governing equations of the homogeneous arch are enriched with convenient distributional terms accounting for the presence of the cracks. Each crack encompasses axial, flexural and shear concentrated deformabilities. The governing equations are then integrated via Laplace transform, thus leading to a solution that is expressed in closed form depending on six boundary conditions only, irrespectively of the number of cracks present along the arch span. Particular solutions for different types of load are obtained. The presented closed-form expressions are duly validated against reference solutions both in terms of kinematics and force distributions presenting an application of a multi-cracked arch subjected to multiple forces as well as the self-weight.