Physical unclonable functions (PUFs) are promising solutions for low-cost device authentication; hence, ignoring the security of PUFs is becoming increasingly difficult. Generally, strong PUFs are vulnerable to classical machine learning (ML) attacks; however, classical ML attacks do not perform well on strong PUFs with complex structures. Side-channel analysis (SCA) hybrid attacks provide efficient approaches to modeling XOR APUF. However, owing to the inadequate exploitation of all available data, recent SCA hybrid attacks may fail on novel PUF designs, such as MPUF and iPUF. Thus, herein, we introduce a method that combines challenge-response pairs with side-channel information to construct challenge-synthetic-feature pairs (CSPs) via feature cross, thereby making it possible to model strong PUFs through multiclass classification. We propose multiclass classification-based SCA hybrid attacks to model strong PUFs with complex structures. When provided with CSPs, the proposed hybrid attacks use a feed-forward neural network with a softmax activation function to build combined models of PUFs. The combined models predict class labels for given challenges and then reveal responses through simple mappings from these labels. Experimental results show that the proposed attacks could model 16-XOR APUF, (128,5)-MPUF, (8,8)-iPUF, and (2,16)-iPUF with accuracies exceeding 94%. Compared with state-of-the-art modeling techniques, the proposed attack has advantages in terms of modeling accuracy, time cost, and the size of required training data.