In this paper, we explore the integration of low-power, low-cost stacked intelligent metasurfaces (SIM) into cell-free (CF) massive multiple-input multiple-output (mMIMO) systems to enhance access point (AP) capabilities and address high power consumption and cost challenges. Specifically, we investigate the uplink performance of a SIM-enhanced CF mMIMO system and propose a novel system framework. First, the closed-form expressions of the spectral efficiency (SE) are obtained using the unique two-layer signal processing framework of CF mMIMO systems. Second, to mitigate inter-user interference, an interference-based greedy algorithm for pilot allocation is introduced. Third, a wave-based beamforming algorithm for SIM is proposed, based only on statistical channel state information, which effectively reduces the fronthaul costs. Finally, a max-min SE power control algorithm is proposed to improve the performance of UE with inferior channel conditions. The results indicate that increasing the number of SIM layers and meta-atoms leads to significant performance improvements and allows for a reduction in the number of APs and AP antennas, thus lowering the costs. In particular, the best SE performance is achieved with the deployment of 20 APs plus 1200 SIM meta-atoms. Finally, the proposed wave-based beamforming algorithm can enhance the SE performance of SIM-enhanced CF-mMIMO systems by 57\%, significantly outperforming traditional CF mMIMO systems.