Whole slide images (WSIs) classification represents a fundamental challenge in computational pathology, where multiple instance learning (MIL) has emerged as the dominant paradigm. Current state-of-the-art (SOTA) MIL methods rely on attention mechanisms, achieving good performance but requiring substantial computational resources due to quadratic complexity when processing hundreds of thousands of patches. To address this computational bottleneck, we introduce EfficientMIL, a novel linear-complexity MIL approach for WSIs classification with the patches selection module Adaptive Patch Selector (APS) that we designed, replacing the quadratic-complexity self-attention mechanisms in Transformer-based MIL methods with efficient sequence models including RNN-based GRU, LSTM, and State Space Model (SSM) Mamba. EfficientMIL achieves significant computational efficiency improvements while outperforming other MIL methods across multiple histopathology datasets. On TCGA-Lung dataset, EfficientMIL-Mamba achieved AUC of 0.976 and accuracy of 0.933, while on CAMELYON16 dataset, EfficientMIL-GRU achieved AUC of 0.990 and accuracy of 0.975, surpassing previous state-of-the-art methods. Extensive experiments demonstrate that APS is also more effective for patches selection than conventional selection strategies.