The paper describes matrix methods whereby the transient voltages and currents produced during switching operations in 3-phase power systems may be evaluated, taking into account appreciable mutual impedances existing between phases of the various items of plant. Operational voltage and impedance matrices are derived which define the transient performance of a network during the clearance of a shunt fault, the individual phases of the circuit-breaker being considered to clear sequentially. The successive constraints imposed upon the network currents are defined by transformation matrices using methods based on the work of Kron. The influence of phase mutual impedances upon the transient over-voltages produced during the isolation of single-phase arcing faults on double-circuit overhead lines is also considered. A simplified mathematical treatment of the effect of circuitbreaker arc restrikes upon the transient response of a power system is described in a concluding Section dealing with resistance switching of overhead-line charging current.