Two-dimensional numerical investigations have been carried out to study the temporal wake characteristics of laminar flow past two identical inline square cylinders performing transverse oscillations. Both the cylinders are forced to perform harmonic oscillations of same frequency and amplitude but with a phase difference. Computations are carried out using commercial software ANSYS Fluent 16.1 on a dynamically sliding mesh for fixed Reynolds number equal to 100. The oscillation frequency is varied from 0.4 to 1.6 times the frequency of vortex shedding behind a single stationary square cylinder. The amplitude of transverse oscillation is kept fixed equal to 0.4D (D = side of the cylinder). In addition, the effect of variation of inter-cylinder spacing has been investigated on wake interference which influences the modes of vortex shedding and resulting dynamic effects on the cylinders. Temporal signals as well as mean characteristics of lift and drag coefficients have been presented for different values of inter-cylinder spacing, phase difference between the two cylinders and frequency of oscillation