•We apply isogeometric collocation techniques to spatial Timoshenko rods.•We solve the strong form equations of the problem in both displacement-based and mixed formulations.•We prove that mixed collocation schemes are locking-free independently of the polynomial degrees for the unknown fields.•Numerical experiments confirm the accuracy and efficiency of the considered methods. In this work we present the application of isogeometric collocation techniques to the solution of spatial Timoshenko rods. The strong form equations of the problem are presented in both displacement-based and mixed formulations and are discretized via NURBS-based isogeometric collocation. Several numerical experiments are reported to test the accuracy and efficiency of the considered methods, as well as their applicability to problems of practical interest. In particular, it is shown that mixed collocation schemes are locking-free independently of the choice of the polynomial degrees for the unknown fields. Such an important property is also analytically proven.