This paper proposes a holographic MIMO (HMIMO) architecture based on stacked intelligent metasurfaces (SIM) for the uplink of cell-free networks. The SIM is employed at the access points (APs) to improve spectral and energy efficiency. The distributed beamforming design involves optimizing the SIM coefficients and local receiver combiner vectors at each AP based on local channel state information (CSI). The central processing unit (CPU) then fuses the local detections from all APs to detect the aggregate multi-user signal. A low-complexity layer-by-layer iterative optimization algorithm is proposed to design the SIM coefficients and combining vectors, maximizing the equivalent channel gain. The weight vector at the CPU is designed based on the minimum mean square error (MMSE) criterion, considering hardware impairments (HWIs). Simulation results demonstrate that the SIM-based HMIMO outperforms conventional single-layer HMIMO in terms of achievable rate, but HWIs limit the achievable rate at high signal-to-noise ratios (SNRs).This paper proposes a holographic MIMO (HMIMO) architecture based on stacked intelligent metasurfaces (SIM) for the uplink of cell-free networks. The SIM is employed at the access points (APs) to improve spectral and energy efficiency. The distributed beamforming design involves optimizing the SIM coefficients and local receiver combiner vectors at each AP based on local channel state information (CSI). The central processing unit (CPU) then fuses the local detections from all APs to detect the aggregate multi-user signal. A low-complexity layer-by-layer iterative optimization algorithm is proposed to design the SIM coefficients and combining vectors, maximizing the equivalent channel gain. The weight vector at the CPU is designed based on the minimum mean square error (MMSE) criterion, considering hardware impairments (HWIs). Simulation results demonstrate that the SIM-based HMIMO outperforms conventional single-layer HMIMO in terms of achievable rate, but HWIs limit the achievable rate at high signal-to-noise ratios (SNRs).