We have carried out laboratory measurements of P-wave velocity and deformation strain during $CO_2$ injection into a porous sandstone sample, in dry and water-saturated conditions. The rock sample was cylindrical, with the axis normal to the bedding plane, and fluid injection was performed from one end. Using a piezoelectric transducer array system, we mapped fluid movement during injection of distilled water into dry sandstone, and of gaseous, liquid, and supercritical $CO_2$ into a water-saturated sample. The velocity changes caused by water injection ranged from $5.61;to;7.52\%$. The velocity changes caused by $CO_2$ injection are typically about $-6\%$, and about $-10\%$ for injection of supercritical $CO_2$, Such changes in velocity show that the seismic method may be useful in mapping $CO_2$ movement in the subsurface. Strain normal to the bedding plane was greater than strain parallel to the bedding plane during $CO_2$ injection; injection of supercritical $CO_2$ showed a particularly strong effect. Strain changes suggest the possibility of monitoring rock mass deformation by using borehole tiltmeters at geological sequestration sites. We also found differences associated with $CO_2$ phases in velocity and strain changes during injection.