Technologies like ultra-massive multiple-input-multiple-output (UM-MIMO) and reconfigurable intelligent surfaces (RISs) are of special interest to meet the key performance indicators of future wireless systems including ubiquitous connectivity and lightning-fast data rates. One of their common features, the extremely large-scale antenna array (ELAA) systems with hundreds or thousands of antennas, give rise to near-field (NF) propagation and bring new challenges to channel modeling and characterization. In this paper, a cross-field channel model for ELAA systems is proposed, which improves the statistical model in 3GPP TR 38.901 by refining the propagation path with its first and last bounces and differentiating the characterization of parameters like path loss, delay, and angles in near- and far-fields. A comprehensive analysis of cross-field boundaries and closed-form expressions of corresponding NF or FF parameters are provided. Furthermore, cross-field experiments carried out in a typical indoor scenario at 300 GHz verify the variation of MPC parameters across the antenna array, and demonstrate the distinction of channels between different antenna elements. Finally, detailed generation procedures of the cross-field channel model are provided, based on which simulations and analysis on NF probabilities and channel coefficients are conducted for $4\times4$, $8\times8$, $16\times16$, and $9\times21$ uniform planar arrays at different frequency bands.