Implementing a queue using a circular buffer
Advice 1

QueueOnCirciularBuffer: you misspelled Circular

Advice 2

Wikipedia gives more canonic names for the data structure. Why not choose, say, CircularBuffer?

Advice 3

Instead of having a single index self.index, why not take two: self.head_index is the index in the underlying storage array holding the head element of the buffer; self.tail_index points into the array location at which next element is inserted. If not efficiency, this adds to maintainability in my opinion.

Advice 4

value = self.buffer[(self.index - self.size+self.max_size)%self.max_size]
self.buffer[(self.index-1+self.max_size)%self.max_size]


Adding self.max_size has not effect since you take the modulo of it.

Advice 5

PEP 8 complains about some aspects of your code layout. Consider using a Python IDE (I use PyCharm); it gives you instant feedback if your code does not adhere to rules in PEP 8.

Advice 6

Its funny that your peak_element returns the tail element of the queue; why not rename it to, say, peak_tail. (And possibly provide peak_head.)

Summa summarum

All in all, I had this in mind:

class CircularBuffer:
    def __init__(self, capacity):
        self.buffer = [0] * capacity
        self.size = 0
        self.capacity = capacity
        self.head_index = 0
        self.tail_index = 0

    def push_element(self, value):
        if self.size == self.capacity:
            raise Exception('The circular buffer is full.')
        self.buffer[self.tail_index] = value
        self.tail_index = (self.tail_index + 1) % self.capacity
        self.size += 1

    def pop_element(self):
        if self.size == 0:
            raise Exception('Popping from an empty circular buffer.')
        ret = self.buffer[self.head_index]
        self.head_index = (self.head_index + 1) % self.capacity
        self.size -= 1
        return ret

    def peek_head(self):
        if self.size == 0:
            raise Exception('Peeking into an empty circular buffer.')
        return self.buffer[self.head_index]


Hope that helps.