Abstract: For superconducting qubit systems, measurements based on a dispersive interaction between the qubit and a cavity is widely used. Progress in implementation of controllable large-scale quantum computers calls for developing higher fidelity and more scalable multi-qubit readout schemes, which require a deeper understanding of the mechanisms by which a measurement of one qubit affects nearby qubits. A starting point is to fully understand readout in two-qubit system. Here, with both full numerical modeling of the system dynamics and analytical techniques, we were able to identify the dominant sources of crosstalk. Our analysis demonstrates that transitions in higher energy levels than are usually modeled play a significant role in the physics of readout. This work suggests promising research directions for more reliable multiqubit readout and provides guidance as to how to optimize either the qubit-qubit detuning or the drive amplitude to reduce crosstalk.