The accuracy of conventional crane engineering problems with bounded uncertainty is limited to cases where only first-order terms are retained. However, the impact of high-order terms on the luffing angular response (LAR) may be significant when it comes to compound functions. A modified first-order compound-function-based interval perturbation method (MFCFIPM) is proposed for the prediction of the LAR field of a dual automobile crane system (DACS) with narrowly bounded uncertainty. In an interval model, all uncertain variables with bounded uncertainty comprise an interval vector. The equilibrium equations of the interval LAR vectors of the DACS are established based on the interval model. The MFCFIPM employs the surface rail generation method to expand the compound-function-based vectors. A modified Sherman–Morrison–Woodbury formula is introduced to analyze the impact of the high-order terms of the Neumann series expansion on the LAR field. Several numerical examples are presented to verify the accuracy and the feasibility of the MFCFIPM. The results show that the MFCFIPM can achieve a better accuracy than the first-order compound-function-based interval perturbation method and a higher efficiency than the Monte Carlo method for the LAR field problem with narrow interval variables. The effects of different numbers of interval variables on the LAR field by the MFCFIPM are also investigated.