We have studied the phase transition of argon in completely filled mesopores. Our effective medium analysis of ultrasonic measurements clearly indicates a continuous phase transition of argon in completely filled pores over a broad temperature range of about 45 K. With decreasing temperature, the amount of frozen argon increases and below about 30 K all adsorbed argon (including the first few layers near the pore wall) is frozen with a shear modulus about equal to the bulk shear modulus. It is remarkable, that in a system showing such a pronounced confinement effect--a continuous phase transition over 45 K--the bulk properties are preserved. A comparison with temperature cycles with one and two adsorbed layers shows, that due to the presence of solid argon in the center of the pores the first few layers are already frozen at a higher temperature (30 K) compared to single layers (20 K). The transfer of our technique from the simple model system that we present in this Letter to other more complex adsorbates and different porous samples should help to enlighten the phase behavior under confinement in further studies.