This paper proposes a method to determine the elastic follow-up factors for the $C(t)$-integral under secondary stress. The rate of creep crack growth for transient creep is correlated with the $C(t)$-integral. Elastic follow-up behavior, which occurs in structures under secondary loading, prevents a relaxation of stress during transient creep. Thus, both the values of $C(t)$ and creep crack growth increase as increasing elastic follow-up. An estimation solution for $C(t)$ was proposed by Ainsworth and Dean based on the reference stress method. To predict the value of $C(t)$ using this solution, an independent method to determine the elastic follow-up factors for cracked bodies is needed. This paper proposed that the elastic follow-up factors for $C(t)$ can be determined by elastic-plastic analyses using the plastic-creep analogy. Finite element analyses were performed to verify this method.