The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of $ k $-cosymplectic geometry. Since these field theories are singular, we need to introduce the notion of $ k $-precosymplectic structure, which is a generalization of the $ k $-cosymplectic structure. Next $ k $-precosymplectic Hamiltonian systems are introduced in order to describe singular field theories, both in Lagrangian and Hamiltonian formalisms. Finally, we develop a constraint algorithm in order to find a submanifold where the existence of solutions of the field equations is ensured. The case of affine Lagrangians is studied as a relevant example.
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