A study was conducted to analyze the sets of vector fields with various shadowing properties of pseudotrajectories. The main difference between the shadowing problem for flows and a similar problem for discrete dynamical systems generated by diffeomorphisms is related to the necessity of reparameterization of shadowing trajectories in the former case. The aim of the study is also to describe the structure of C¹ interiors of sets of vector fields with various shadowing properties. A monotonically increasing homeomorphism h of the line R such as h(0) = 0 is called a reparameterization. The study analyzed that a field X has the Lipschitz shadowing property if there exist certain numbers with particular properties. The study also concludes that a field X has the orbital shadowing property if there exists a number with a particular property.