Eddy-currents are generated in MRI scanners’ metallic structures due to the rapid switching of gradient coils. They may result in image distortions and induce acoustic-noise particularly for fast/spiral sequences. Transient eddy-currents computations can be used to understand the extent of such effects. In this work, a numerical framework was devised to compute transient eddy-currents induced by an amplitude-modulated sinusoidal pulse for a longitudinal gradient coil configuration. Stream functions representation of eddy-currents, Multilayer Integral Method, and an excitation current with amplitude-modulated sinusoidal function are used to solve the circuit equation and efficiently compute transient eddy-currents generated in the cryostat.