A method for producing a vitreous silica crucible made of a transparent inner layer containing inner layer bubbles and an outer layer containing outer layer bubbles, comprising: depositing quartz powder on inner surface of a rotating mold, heating the quartz powder layer to melt and vitrify the quartz powder layer by arc electrodes, and vacuuming at the time of melting by a depressurizing mechanism including depressurizing passages to suck the bubbles in the inner layer, thereby forming the transparent inner layer, wherein the pressure inside the mold is set to a range of 50 kPa to 200 kPa by an atmospheric pressure control, the depressurizing condition using the depressurizing passages is set to the range of 40 kPa to 100 kPa, the power supplied to the arc electrodes is in the output range of 300 kVA to 12,000 kVA, the electrode length consumed per unit time of arc discharge is about 2mm per minute, and the arc melting is made in a state where the center position of the electrode and the rotation center of the mold are matched with each other, and wherein the vitreous silica crucible is suitable for pulling up silicon single crystals by a first stage and a second stage after the first stage, wherein the first stage starts from the beginning of heating silicon filled in the crucible and ends when a necking step of forming a necking portion is finished; and the second stage starts from the end of the necking step and ends at the end of the pulling-up process; wherein a second stage expansion coefficient X2 of the inner-layer bubbles during the second stage is set to 1/3 or less of a first stage expansion coefficient X1 of the inner-layer bubbles during the first stage; and a second stage expansion coefficient Y2 of the outer-layer bubbles during the second stage is set to 1/2 or less of a first stage expansion coefficient Y1 of the outer-layer bubbles during the first stage. depositing quartz powder on inner surface of a rotating mold, heating the quartz powder layer to melt and vitrify the quartz powder layer by arc electrodes, and vacuuming at the time of melting by a depressurizing mechanism including depressurizing passages to suck the bubbles in the inner layer, thereby forming the transparent inner layer, wherein the pressure inside the mold is set to a range of 50 kPa to 200 kPa by an atmospheric pressure control, the depressurizing condition using the depressurizing passages is set to the range of 40 kPa to 100 kPa, the power supplied to the arc electrodes is in the output range of 300 kVA to 12,000 kVA, the electrode length consumed per unit time of arc discharge is about 2mm per minute, and the arc melting is made in a state where the center position of the electrode and the rotation center of the mold are matched with each other, and wherein the vitreous silica crucible is suitable for pulling up silicon single crystals by a first stage and a second stage after the first stage, wherein the first stage starts from the beginning of heating silicon filled in the crucible and ends when a necking step of forming a necking portion is finished; and the second stage starts from the end of the necking step and ends at the end of the pulling-up process; wherein a second stage expansion coefficient X2 of the inner-layer bubbles during the second stage is set to 1/3 or less of a first stage expansion coefficient X1 of the inner-layer bubbles during the first stage; and a second stage expansion coefficient Y2 of the outer-layer bubbles during the second stage is set to 1/2 or less of a first stage expansion coefficient Y1 of the outer-layer bubbles during the first stage.