A new spatial block-correlation model for fluid antenna systems is proposed to accurately approximate the spatial correlation in fluid antenna systems (FAS) while maintaining analytical tractability. The model is based on the block-diagonal approximation of the spatial correlation matrix, motivated by the block-fading assumption and statistical results on large correlation matrices. The proposed block-correlation model closely approximates the results obtained with realistic models such as Jakes's and Clarke's. The framework is applied to analyze fluid antenna multiple access (FAMA) systems, evaluating their performance for both one- and two-dimensional fluid antennas. The model enables tractable performance analysis and provides insights into the multiplexing capabilities of FAS. The key contributions include: (1) a block-diagonal spatial correlation model that balances accuracy and tractability, (2) an algorithm to efficiently approximate the FAS correlation structure based on the block-diagonal framework, (3) application of the model to slow-FAMA systems, yielding tractable expressions for the outage probability (OP), and (4) performance evaluation of slow-FAMA, highlighting the benefits of oversampling, multiplexing capacity, and the ability of the block-correlation model to capture different effects inherent to FAS. The model is validated through simulations and comparisons with existing correlation models, demonstrating its effectiveness in capturing the spatial correlation characteristics of FAS.A new spatial block-correlation model for fluid antenna systems is proposed to accurately approximate the spatial correlation in fluid antenna systems (FAS) while maintaining analytical tractability. The model is based on the block-diagonal approximation of the spatial correlation matrix, motivated by the block-fading assumption and statistical results on large correlation matrices. The proposed block-correlation model closely approximates the results obtained with realistic models such as Jakes's and Clarke's. The framework is applied to analyze fluid antenna multiple access (FAMA) systems, evaluating their performance for both one- and two-dimensional fluid antennas. The model enables tractable performance analysis and provides insights into the multiplexing capabilities of FAS. The key contributions include: (1) a block-diagonal spatial correlation model that balances accuracy and tractability, (2) an algorithm to efficiently approximate the FAS correlation structure based on the block-diagonal framework, (3) application of the model to slow-FAMA systems, yielding tractable expressions for the outage probability (OP), and (4) performance evaluation of slow-FAMA, highlighting the benefits of oversampling, multiplexing capacity, and the ability of the block-correlation model to capture different effects inherent to FAS. The model is validated through simulations and comparisons with existing correlation models, demonstrating its effectiveness in capturing the spatial correlation characteristics of FAS.