Let us consider flat electro-magnetic wave propagating in the positive direction along the axis x. In this case the equation of such a wave can be written as:

Ex = 0,    Ey = E0cos(wt - kx),  Ez = 0; Hx = 0,   Hy = 0, Hz = H0cos(wt - kx);

where k=w/c is the wave constant, c is the velocity of the light. As we can see from the animation there is no oscillation of electric and magnetic components of wave in the direction x (E_x= H_x = 0). This means the the electromagnetic wave is the transverse one. This is one of the principle differences of electromagnetic wave as compared to the wave of mechanical stresses. Another principle of electro-magnetic wave propagation is that the vectors E and H oscillate in phase, i.e. they achieve the maximum value in the same points of the space.