There is something seriously wrong. As a matter of urgency you should have the dryer and/or your electrical supply checked by a professional electrician.
If your dryer is correctly connected then there is a high chance that there is a short circuit within your dryer. There may be a danger of electrocution if touching any metal part of the dryer (which is why your electrical system keeps switching off - it is trying to prevent you getting fried).
Less alarmingly - the dryer may simply be connected to the wrong circuit. Dryers pull a lot of power and if connected to a standard power ring may push the total (for all the items on the ring) above the limit for that ring. Most houses have a high power ring for cookers and the like - you may need to connect to this ring instead (consult an electrician). An overloaded electrical ring can cause a fire (if the safeties fail to switch off the circuit).
Hardly worrying at all. Your electrical safeties may be overly sensitive. Electrical devices often cause a surge when switched on which rapidly settles down to a reasonable drain. Most trip switches have a delay built into them to allow for brief surges. Your system may be overly sensitive.
In any case - consult an electrician.
Mark, April 2005