Is ideal band pass filter (brick wall filter) linear phase?
Assuming you are refering to LTI (linear time-invariant) systems to implement the filter. 

The impulse response $h[n]$ of the ideal brickwall bandpass filter :
$$H(\omega) = \begin{cases} 1 ~~~,~~~ |\omega-\omega_c|&lt;W \\ 0 ~~~,~~~\text{o.w.}\\ \end{cases}$$ 
is 
$$
h[n] = 2 \cos(\omega_c n) \frac{ \sin(W n) }{ \pi n }
$$

which is real and even symetric about origin; i.e., $h[n] = h[-n]$,  hence it's a zero-phase (in the passband), but noncausal filter. 

When this impulse response is truncated and shifted right enough to make it causal: $h_c[n] = h[n-d]$ then the resulting bandpass filter will be linear phase in the passband: 
$$ H_c(\omega)= e^{-j\omega d} H(\omega)$$ with a linear phase term of $$\phi(\omega) = -\omega d$$

The phase is not defined for those frequencies where the frequency response is zero. 

Note that the truncated filter is no more the ideal filter. Also note that you cannot shift the ideal filter to make it causal (requires infinite shift). And finally note that the zero-phase ideal filter is also a linear phase filter.