Fluid injection experiments into a Hele-Shaw cell filled with agar gels were carried out at a constant injection pressure. Agar gels of concentration of 0.1wt%, 0.2wt%, and 0.3wt% agar were used as a model material with visco-elastic properties. In the case of lower concentration of agar, agar gels behave as a viscous fluid. However, the property of agar gels as elastic solids increases with increasing concentration of agar. The ratio of relative tensile strength among agar gels of concentration of 0.1wt%, 0.2wt%, and 0.3wt% agar resulted from indentation experiments are 0.14:1.0:3.9. Growth patterns obtained by our Hele Shaw cell experiments are classified into three typical patterns. They are patterns generated by viscous fingering, visco-elastic fingering, and single plane cracking. A visco-elastic fingering is new pattern formation observed in the fluid injection experiments into visco-elastic materials. The characteristics of the visco-elastic fingering pattern are following. 1) The visco-elastic fingering pattern has a branched structure same as one of the viscous fingering pattern. 2) The visco-elastic fingering pattern has an acute growing tip similar to that of single plane cracking, though a shape of growing tip of viscous fingering is round. The phase diagram for the Hele-Shaw cell experiment filed with the agar gel is obtained by changing both the pressure of air injection and the concentration of agar systematically. Fluid intrusion phenomena into visco-elastic materials often occur in geophysical process: e. g., magma migration, core formation, fluid migration in accretionary prisms, etc. Our results will give us new implications for the geophysical process in which the earth or planet's materials behave as visco-elastic materials.