In the past few decades, optical transport networks (OTNs) have undergone significant evolution, from the earliest wavelength-division multiplexing (WDM) OTNs to elastic optical networks (EONs) and later to space-division multiplexing (SDM) OTNs, to address the continuous growth of Internet traffic. By 2024, Pbps-level OTNs are expected, far exceeding the capacity limit of single-mode fibers. The massive SDM era is on the horizon. In this context, newly designed OTNs called spatial channel networks (SCNs), which achieve high cost efficiency by means of practical hierarchical optical cross-connects, have recently been proposed. However, the evolution of OTNs will simultaneously present challenges related to resource allocation in networking. For instance, with the evolution from WDM-OTNs to EONs, the resource allocation problem was transformed from the routing and wavelength assignment (RWA) problem to the routing and spectrum assignment (RSA) problem due to the additionally introduced constraint of spectrum contiguity. Similarly, specially designed algorithms are also expected to be essential for addressing the resource allocation problem in SCNs. In this paper, we define this new problem as the routing, spatial channel, and spectrum assignment (RSCSA) problem. We propose an integer linear programming (ILP) model and a heuristic algorithm to solve the RSCSA problem. We examine the performance of the proposed approaches via simulation experiments. The results show that both proposed approaches are effective in finding the optimal solutions or solutions close to the lower bounds. To the best of our knowledge, this is the first work to focus on the problem of resource allocation in SCNs.